Middle School Math Quiz: Understand Line Segment Transformation Properties

20 questions · exam conditions

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Understand Line Segment Transformation PropertiesQuestion 1 of 20

A line segment undergoes a sequence of transformations: first a reflection across the x-axis, then a 180° rotation about the origin. If the original segment has length $\sqrt{13}$ units, what is the length of the final transformed segment?

\frac{\sqrt{13}}{2}

units because the transformations reduced the segment by half each time

2\sqrt{13}

units because two transformations were applied to the original segment

\sqrt{13}

units because both transformations preserve segment lengths individually

13

units because the length is squared when two transformations are composed

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Middle School Math Quiz

Middle School Math Quiz: Understand Line Segment Transformation Properties

Practice Understand Line Segment Transformation Properties in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Understand Line Segment Transformation Properties, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

$\frac{\sqrt{13}}{2}$ units because the transformations reduced the segment by half each time
$2\sqrt{13}$ units because two transformations were applied to the original segment
$\sqrt{13}$ units because both transformations preserve segment lengths individually (correct answer)
$13$ units because the length is squared when two transformations are composed

Explanation: When you encounter problems involving sequences of transformations, the key concept to remember is that certain transformations preserve distances and lengths, while others do not. Both reflections and rotations are called rigid transformations or isometries, which means they preserve all distances and lengths. When you reflect a line segment across the x-axis, every point moves to a new location, but the distance between any two points stays exactly the same. Similarly, when you rotate a segment 180° about the origin, the segment moves to a new position but maintains its original length. Since both transformations in this sequence preserve length individually, the final segment will have the same length as the original:

\sqrt{13}

units. Let's examine why the other answers are incorrect: Choice A incorrectly assumes that each transformation reduces the segment length by half. This would only be true for scaling transformations with a scale factor of

\frac{1}{2}

, not for reflections and rotations. Choice B applies faulty reasoning that multiple transformations automatically change the length. The number of transformations doesn't determine length changes—the type of transformation does. Choice D makes an error by squaring the original length, possibly confusing length with area or misunderstanding how transformations compose. Study tip: Remember that rigid transformations (reflections, rotations, and translations) always preserve lengths, angles, and shapes. Only scaling transformations change lengths. When you see transformation problems, first identify whether the transformations are rigid or not.

Question 2

Triangle ABC is rotated 90° clockwise about point P to form triangle A'B'C'. If side AB has length 7 cm and side BC has length 5 cm, what can be concluded about the corresponding sides in triangle A'B'C'?

Side A'B' has length 7 cm and side B'C' has length 5 cm (correct answer)
Side A'B' has length 5 cm and side B'C' has length 7 cm
The lengths cannot be determined without knowing the position of point P
The side lengths are proportional but not necessarily equal to the original lengths

Explanation: Under rotations, line segments map to line segments of the same length. Therefore, AB maps to A'B' with the same length (7 cm), and BC maps to B'C' with the same length (5 cm). Choice B incorrectly swaps the lengths. Choice C incorrectly suggests that the position of the rotation point affects lengths. Choice D incorrectly applies properties of similarity transformations rather than rigid transformations.

Question 3

Segment $\overline{ST}$ has endpoints $S(0,0)$ and $T(6,8)$ . It is reflected over the $x$ -axis to form $\overline{S'T'}$ . What is the length of $\overline{S'T'}$ ?

$14$ units
$\sqrt{28}$ units
$8$ units
$10$ units (correct answer)

Explanation: This question tests understanding that rotations, reflections, and translations preserve line segment lengths—rigid transformations move segments without stretching or compressing. Rigid transformations (rotation, reflection, translation) preserve distances: segment AB with length d=√((x₂-x₁)²+(y₂-y₁)²) transforms to A'B' with equal length d'=d. Example: AB from (1,2) to (4,6) has length √(9+16)=5, translation by (+3,+2) gives A'(4,4) to B'(7,8) with length √(9+16)=5 unchanged. Property holds for all three transformations (move/flip/turn but don't resize). For this reflection over the x-axis, original ST length is √[(6-0)² + (8-0)²] = √[36+64] = 10, and after reflection, S'(0,0) to T'(6,-8) has length √[(6-0)² + (-8-0)²] = √[36+64] = 10, confirming preservation. The length is 10 units, unchanged. A common error is calculating only partial differences, like √[36+16]=√52 or something leading to 14 if adding wrong. To verify: (1) calculate original length, (2) negate y-coordinates, (3) calculate image length, (4) compare—equal. All rigid transformations preserve length because they maintain distances (isometries: distance-preserving transformations)—the segment flips but not size.

Question 4

A student says: "If you rotate a segment $90^\circ$ , its length might change because it points in a different direction." Which statement best corrects the student?

The student is incorrect; rotations always double the length.
The student is correct only if the rotation is about the origin.
The student is correct; diagonal segments change length when rotated.
The student is incorrect; rotations are rigid transformations that preserve length. (correct answer)

Explanation: This question tests understanding that rotations, reflections, and translations preserve line segment lengths—rigid transformations move segments without stretching or compressing. Rigid transformations (rotation, reflection, translation) preserve distances: segment AB with length d=√((x₂-x₁)²+(y₂-y₁)²) transforms to A'B' with equal length d'=d. Example: AB from (1,2) to (4,6) has length √(9+16)=5, translation by (+3,+2) gives A'(4,4) to B'(7,8) with length √(9+16)=5 unchanged. Property holds for all three transformations (move/flip/turn but don't resize). The student's claim is incorrect because rotations preserve lengths regardless of direction; for example, rotating (0,0) to (3,4) by 90° gives (0,0) to (-4,3), both lengths √[9+16]=5. The best correction is that rotations are rigid transformations that preserve length. A common error is thinking direction changes length, like claiming it doubles. To verify the concept: (1) calculate original length, (2) apply rotation rules, (3) calculate image length, (4) compare—always equal for rigid motions. All rigid transformations preserve length because they maintain distances (isometries: distance-preserving transformations)—the segment turns but not size.

Question 5

Segment $CD$ has endpoints $C(-2,5)$ and $D(4,5)$ . The segment is reflected over the $y$ -axis to form $C'D'$ . How does the length of $C'D'$ compare to the length of $CD$ ?

The length doubles.
The length stays the same. (correct answer)
The length changes because the segment moves to negative $x$ -values.
The length is cut in half.

Explanation: This question tests understanding that rotations, reflections, and translations preserve line segment lengths—rigid transformations move segments without stretching or compressing. Rigid transformations (rotation, reflection, translation) preserve distances: segment AB with length d=√((x₂-x₁)²+(y₂-y₁)²) transforms to A'B' with equal length d'=d. For segment CD from (-2,5) to (4,5), original length is √((4 - (-2))² + (5-5)²) = √36 = 6; after reflection over y-axis, C'(2,5) to D'(-4,5), length √((-4-2)² + (5-5)²) = √36 = 6. The correct statement is that the length stays the same, as reflection flips the segment but preserves distances. A common error is thinking reflection changes length due to negative x-values, but coordinates' signs don't affect distance calculation. To verify: (1) calculate original length with distance formula, (2) apply reflection by negating x-coordinates, (3) calculate image length, (4) compare—they match. All rigid transformations preserve length because they are isometries: distance-preserving transformations that move the segment's position or orientation but not its size. Another error is assuming horizontal segments halve or double when reflected, ignoring that only position changes.

Question 6

Segment $\overline{CD}$ has endpoints $C(-2,1)$ and $D(4,1)$ . It is reflected over the $y$ -axis to form $\overline{C'D'}$ . How does the length of $\overline{C'D'}$ compare to the length of $\overline{CD}$ ?

It is longer because the segment moves to the other side of the axis.
It is half as long.
It is shorter because some coordinates become negative.
It is the same length. (correct answer)

Explanation: This question tests understanding that rotations, reflections, and translations preserve line segment lengths—rigid transformations move segments without stretching or compressing. Rigid transformations (rotation, reflection, translation) preserve distances: segment AB with length d=√((x₂-x₁)²+(y₂-y₁)²) transforms to A'B' with equal length d'=d. Example: AB from (1,2) to (4,6) has length √(9+16)=5, translation by (+3,+2) gives A'(4,4) to B'(7,8) with length √(9+16)=5 unchanged. Property holds for all three transformations (move/flip/turn but don't resize). For this reflection over the y-axis, original CD length is √[(4 - (-2))² + (1-1)²] = √[36+0] = 6, and after reflection, C'(2,1) to D'(-4,1) has length √[(-4-2)² + (1-1)²] = √[36+0] = 6, confirming equal lengths. The lengths are the same, as reflections preserve distances. A common error is thinking negative coordinates shorten the segment, like claiming it's shorter. To verify: (1) calculate original length with distance formula, (2) apply reflection by negating x-coordinates, (3) calculate image length, (4) compare—they match. All rigid transformations preserve length because they maintain distances (isometries: distance-preserving transformations)—the segment flips but not size.

Question 7

Segment $\overline{QR}$ has endpoints $Q(-4,0)$ and $R(-1,4)$ . It is translated by $(+5,-3)$ and then reflected over the $y$ -axis to form $\overline{Q''R''}$ . What is the length of $\overline{Q''R''}$ ?

$5$ units (correct answer)
$\sqrt{5}$ units
$7$ units
$\sqrt{25}$ units

Explanation: This question tests understanding that rotations, reflections, and translations preserve line segment lengths—rigid transformations move segments without stretching or compressing. Rigid transformations (rotation, reflection, translation) preserve distances: segment AB with length d=√((x₂-x₁)²+(y₂-y₁)²) transforms to A'B' with equal length d'=d. Example: AB from (1,2) to (4,6) has length √(9+16)=5, translation by (+3,+2) gives A'(4,4) to B'(7,8) with length √(9+16)=5 unchanged. Property holds for all three transformations (move/flip/turn but don't resize). For these combined transformations, original QR from (-4,0) to (-1,4) has length √((-1-(-4))²+(4-0)²)=√(9+16)=5, after translation to (1,-3) and (4,1), then reflection to (-1,-3) and (-4,1), with length √((-4-(-1))²+(1-(-3))²)=√(9+16)=5. This verifies the length preservation, as the correct answer is 5 units, matching the unchanged distance. A common error is misapplying steps (e.g., reflecting first, getting wrong points leading to √5 or 7), or using addition for distance giving 7. Verifying: (1) calculate original length with distance formula, (2) apply translation then reflection step-by-step, (3) calculate final image length, (4) compare (should equal). All rigid transformations preserve length because they maintain distances (isometries: distance-preserving transformations)—segment moves position/orientation but not size.

Question 8

Segment $\overline{GH}$ has endpoints $G(-1,-2)$ and $H(3,1)$ . It is rotated $180^\circ$ about the origin to form $\overline{G'H'}$ . Which statement is true about the lengths of $\overline{GH}$ and $\overline{G'H'}$ ?

$\overline{G'H'}$ is half the length of $\overline{GH}$ .
$\overline{G'H'}$ has the same length as $\overline{GH}$ . (correct answer)
$\overline{G'H'}$ is twice the length of $\overline{GH}$ .
$\overline{G'H'}$ is 2 units longer than $\overline{GH}$ .

Explanation: This question tests understanding that rotations, reflections, and translations preserve line segment lengths—rigid transformations move segments without stretching or compressing. Rigid transformations (rotation, reflection, translation) preserve distances: segment AB with length d=√((x₂-x₁)²+(y₂-y₁)²) transforms to A'B' with equal length d'=d. Example: AB from (1,2) to (4,6) has length √(9+16)=5, translation by (+3,+2) gives A'(4,4) to B'(7,8) with length √(9+16)=5 unchanged. Property holds for all three transformations (move/flip/turn but don't resize). For this specific 180° rotation about the origin, original GH from (-1,-2) to (3,1) has length √((3-(-1))²+(1-(-2))²)=√(16+9)=5, and after rotation, G' is (1,2) and H' is (-3,-1), with length √((-3-1)²+(-1-2)²)=√(16+9)=5. This verifies the length preservation, as the correct statement is that G'H' has the same length as GH. A common error is claiming rotation changes the length (e.g., doubles to twice or adds 2 units), using wrong formula like |3-(-1)| + |1-(-2)| =7 instead of sqrt, or incorrect 180° rule giving wrong points then different length. Verifying: (1) calculate original length with distance formula, (2) apply rotation using (x,y) to (-x,-y), (3) calculate image length with the same formula, (4) compare (should equal). All rigid transformations preserve length because they maintain distances (isometries: distance-preserving transformations)—segment moves position/orientation but not size.

Question 9

Segment $\overline{LM}$ has endpoints $L(5,-1)$ and $M(2,-5)$ . It is reflected over the $x$ -axis to form $\overline{L'M'}$ . What is the length of $\overline{L'M'}$ ?

$5$ units
$7$ units
$\sqrt{41}$ units
$\sqrt{25}$ units (correct answer)

Explanation: This question tests understanding that rotations, reflections, and translations preserve line segment lengths—rigid transformations move segments without stretching or compressing. Rigid transformations (rotation, reflection, translation) preserve distances: segment AB with length d=√((x₂-x₁)²+(y₂-y₁)²) transforms to A'B' with equal length d'=d. Example: AB from (1,2) to (4,6) has length √(9+16)=5, translation by (+3,+2) gives A'(4,4) to B'(7,8) with length √(9+16)=5 unchanged. Property holds for all three transformations (move/flip/turn but don't resize). For this specific reflection over the x-axis, original LM from (5,-1) to (2,-5) has length √((2-5)²+(-5-(-1))²)=√(9+16)=5, and after reflection, L' is (5,1) and M' is (2,5), with length √((2-5)²+(5-1)²)=√(9+16)=5. This verifies the length preservation, as the correct answer is √25 units (which is 5), matching the unchanged distance. A common error is claiming reflection changes length (e.g., to √41 from wrong dy), using |2-5| + | -5 - (-1)|=7, or wrong reflection rule like over y-axis giving incorrect points then wrong length. Verifying: (1) calculate original length with distance formula, (2) apply reflection by negating y-coordinates, (3) calculate image length with the same formula, (4) compare (should equal). All rigid transformations preserve length because they maintain distances (isometries: distance-preserving transformations)—segment moves position/orientation but not size.

Question 10

In the coordinate plane shown, line segment PQ is translated 4 units right and 3 units down to form line segment P'Q'. What is the relationship between the lengths of PQ and P'Q'?

P'Q' is longer than PQ because the translation moved the segment farther from the origin
P'Q' is shorter than PQ because translations compress geometric figures
P'Q' has the same length as PQ because translations preserve segment lengths (correct answer)
The relationship depends on whether the translation vector is parallel to segment PQ

Explanation: Under translations, line segments map to line segments of the same length. This is true regardless of the direction or magnitude of the translation vector. Choice A incorrectly relates segment length to distance from origin. Choice B incorrectly suggests translations compress figures. Choice D incorrectly suggests the direction of translation affects segment length preservation.

Question 11

Triangle PQR undergoes a 270° clockwise rotation about vertex P to form triangle PQ'R'. If side QR has length 12 units, which statement about the transformed triangle is correct?

Side Q'R' has length 12 units only because the rotation is about vertex P of the triangle
Side PQ' has length 12 units because Q'R' corresponds to the original side PQ
Side Q'R' has length greater than 12 units because 270° rotation stretches the figure
Side Q'R' has length 12 units because rotations about any point preserve segment lengths (correct answer)

Explanation: When you encounter questions about geometric transformations, focus on what properties are preserved versus what changes during the transformation. Rotations are rigid transformations, meaning they preserve all distances and angle measures regardless of the rotation angle or center point. When triangle PQR rotates 270° clockwise about vertex P, every point moves along a circular arc, but the distances between any two points remain exactly the same. Since side QR has length 12 units in the original triangle, the corresponding side Q'R' in the rotated triangle must also have length 12 units. Let's examine why the other options are incorrect. Choice A suggests the length is preserved "only because" the rotation is about vertex P, but this misses the key point—rotations preserve distances regardless of which point serves as the center. Choice B incorrectly claims that Q'R' corresponds to side PQ, when actually Q'R' corresponds to the original side QR. The lengths would only match if PQ happened to equal QR. Choice C reflects a common misconception that rotations stretch figures like some other transformations do, but rotations never change distances—they only change position and orientation. The correct answer is D because rotations preserve segment lengths no matter what angle of rotation or center point you use. This is a fundamental property of rigid transformations. Study tip: Remember that rigid transformations (rotations, reflections, translations) always preserve distances and angles. Only non-rigid transformations like dilations change lengths.

Question 12

In the figure, line segment ST is reflected across line m to create line segment S'T'. Point X lies on segment ST such that SX = 6 units and XT = 4 units. What is the length of segment S'X'?

6 units because point S maps to point S' and point X maps to point X' (correct answer)
4 units because the reflection reverses the order of points on the segment
10 units because S'X' represents the total length of the original segment ST
The length depends on the distance between line ST and the line of reflection m

Explanation: Under reflections, line segments map to line segments of the same length. Since SX has length 6 units, its image S'X' must also have length 6 units. Choice B incorrectly uses the length of XT and misunderstands how reflections preserve order. Choice C incorrectly uses the total segment length. Choice D incorrectly suggests that distance to the reflection line affects segment length.

Question 13

A line segment AB is reflected across line j, then the resulting segment A'B' is translated 5 units left to form segment A''B''. If the original segment AB has length $2\sqrt{5}$ units, what is the length of segment A''B''?

$2\sqrt{5} - 5$ units because the translation moved the segment 5 units in the negative direction
$2\sqrt{5}$ units because both reflection and translation preserve segment lengths throughout the sequence (correct answer)
$2\sqrt{5} + 5$ units because the total transformation adds 5 units to the original length
$\sqrt{(2\sqrt{5})^2 + 5^2}$ units because the transformations create a right triangle relationship

Explanation: When you encounter transformation problems, the key concept to remember is that certain transformations preserve distance while others don't. Reflections and translations are both rigid transformations, meaning they move figures without changing their size or shape. Let's trace through this problem step by step. The original segment AB has length

2\sqrt{5}

units. When AB is reflected across line j, the resulting segment A'B' maintains exactly the same length as the original because reflection acts like flipping the segment over a mirror line—the distance between the endpoints stays identical. Then, when A'B' is translated 5 units left to create A''B'', translation simply slides the entire segment to a new position without stretching or shrinking it. Looking at the wrong answers: Choice A incorrectly assumes that moving 5 units left somehow subtracts from the segment's length, confusing the direction of movement with the measurement of the segment itself. Choice C makes the opposite error, thinking the translation adds to the length. Choice D applies the Pythagorean theorem as if the transformations created some kind of right triangle, which completely misunderstands what's happening—we're measuring the length of the final segment, not the distance between original and final positions. The answer is B:

2\sqrt{5}

units because both transformations preserve length. Study tip: Remember that reflections, rotations, and translations are rigid transformations that preserve all distances and angles. Only dilations (scaling) change the size of geometric figures.

Question 14

A line segment on grid paper has endpoints $G(-1,-3)$ and $H(3,0)$ . It is reflected over the $x$ -axis to form $\overline{G'H'}$ . What is the length of $\overline{G'H'}$ ?

$3$ units
$4$ units
$5$ units (correct answer)
$7$ units

Explanation: This question tests understanding that rotations, reflections, and translations preserve line segment lengths—rigid transformations move segments without stretching or compressing. Rigid transformations (rotation, reflection, translation) preserve distances: segment AB with length d=√((x₂-x₁)²+(y₂-y₁)²) transforms to A'B' with equal length d'=d. Example: AB from (1,2) to (4,6) has length √(9+16)=5, translation by (+3,+2) gives A'(4,4) to B'(7,8) with length √(9+16)=5 unchanged. Property holds for all three transformations (move/flip/turn but don't resize). For this reflection over the x-axis, original GH length is √[(3 - (-1))² + (0 - (-3))²] = √[16+9] = 5, and after reflection, G'(-1,3) to H'(3,0) has length √[(3 - (-1))² + (0-3)²] = √[16+9] = 5, confirming the same. The length is 5 units, as expected for rigid transformations. A common error is using taxicab distance like |3 - (-1)| + |0 - (-3)| = 7, picking 7 units. To verify: (1) calculate original length, (2) apply reflection by negating y-coordinates, (3) calculate image length, (4) compare—identical. All rigid transformations preserve length because they maintain distances (isometries: distance-preserving transformations)—the segment flips but not size.

Question 15

Rectangle ABCD is translated to form rectangle A'B'C'D'. If diagonal AC has length 10 cm, what must be true about diagonal A'C' in the translated rectangle?

The length of diagonal A'C' depends on the direction and distance of the translation vector
Diagonal A'C' has length 10 cm because the rectangle's shape determines the diagonal length
Diagonal A'C' has a different length because translations change the internal structure of figures
Diagonal A'C' has length 10 cm because translations preserve all segment lengths within figures (correct answer)

Explanation: When you encounter questions about transformations like translations, the key concept to remember is that translations are rigid transformations—they move figures without changing their size or shape. A translation slides every point of a figure the same distance in the same direction. Since rectangle ABCD is simply moved to a new position to form A'B'C'D', all the measurements within the rectangle remain exactly the same. This includes side lengths, angles, and crucially, diagonal lengths. If diagonal AC measures 10 cm in the original rectangle, then diagonal A'C' must also measure 10 cm because translations preserve all distances and measurements within figures. Let's examine why the other answers are incorrect. Choice A suggests the diagonal length depends on the translation vector's direction and distance, but this confuses the movement of the rectangle's position with changes to its internal measurements—translations don't alter any lengths within the figure. Choice B reaches the correct conclusion but gives an incomplete reason; while the rectangle's shape does determine diagonal length, this doesn't explain why translation preserves that measurement. Choice C contains a fundamental misconception, claiming translations change internal structure, which contradicts the definition of rigid transformations. The correct answer is D because it accurately states both the result (10 cm diagonal) and the complete reasoning (translations preserve all segment lengths). Study tip: Remember that translations, rotations, and reflections are all rigid transformations—they preserve size, shape, and all internal measurements. Only dilations change lengths.

Question 16

Segment $NP$ has endpoints $N(2,7)$ and $P(6,2)$ . It is reflected over the line $y=x$ to form $N'P'$ . What is the length of $N'P'$ ?

$41$
$\sqrt{41}$ (correct answer)
$9$
$\sqrt{5}$

Question 17

Segment $LM$ has endpoints $L(-1,-4)$ and $M(3,-4)$ . It is rotated $180^\circ$ about the origin to form $L'M'$ . What is the length of $L'M'$ ?

$\sqrt{32}$
$4$ (correct answer)
$-4$
$8$

Question 18

On a coordinate plane, segment $\overline{AB}$ has endpoints $A(1,2)$ and $B(4,6)$ . The segment is translated by $(+3,+2)$ to form $\overline{A'B'}$ . What is the length of $\overline{A'B'}$ ?

10 units
7 units
5 units (correct answer)
2.5 units

Explanation: This question tests understanding that rotations, reflections, and translations preserve line segment lengths—rigid transformations move segments without stretching or compressing. Rigid transformations (rotation, reflection, translation) preserve distances: segment AB with length d=√((x₂-x₁)²+(y₂-y₁)²) transforms to A'B' with equal length d'=d. Example: AB from (1,2) to (4,6) has length √(9+16)=5, translation by (+3,+2) gives A'(4,4) to B'(7,8) with length √(9+16)=5 unchanged. Property holds for all three transformations (move/flip/turn but don't resize). For this specific translation, original AB length is √[(4-1)² + (6-2)²] = √[9+16] = 5, and after translation, A'(4,4) to B'(7,8) has length √[(7-4)² + (8-4)²] = √[9+16] = 5, confirming preservation. The correct answer is 5 units, as the length remains unchanged. A common error is miscalculating the distance by adding instead of using the formula, like claiming 7 units from incorrect addition of differences. To verify: (1) calculate original length with distance formula, (2) apply translation by adding (+3,+2) to each coordinate, (3) calculate image length with the same formula, (4) compare—they are equal. All rigid transformations preserve length because they maintain distances (isometries: distance-preserving transformations)—the segment moves position but not size.

Question 19

Segment $\overline{JK}$ has endpoints $J(3,2)$ and $K(7,5)$ . It is translated by $(-4, 1)$ to form $\overline{J'K'}$ . Which statement is true?

The length stays the same: $J'K'=JK$ . (correct answer)
$\overline{J'K'}$ is shorter because the translation includes a negative number.
$\overline{J'K'}$ is longer because the points moved.
The length changes unless the segment is horizontal or vertical.

Explanation: Translations are rigid transformations: they move every point by the same vector without changing distances, so segment length is always preserved. For

\overline{JK}

JK = \sqrt{(7-3)^2 + (5-2)^2} = \sqrt{16+9} = 5

. After translating by

(-4, 1)

J'(-1, 3)

and

K'(3, 6)

, so

J'K' = \sqrt{(3-(-1))^2 + (6-3)^2} = \sqrt{16+9} = 5

. Choice B is incorrect because a negative translation component indicates direction, not shrinkage. Choice C is incorrect because moving points does not change the distance between them. Choice D is incorrect because translation preserves length regardless of orientation.

Question 20

A student draws segment $QR$ from $Q(-4,-2)$ to $R(-1,2)$ . Then the student translates it by $(+5,-3)$ and reflects the result over the $y$ -axis to get $Q''R''$ . What is the length of $Q''R''$ ?

$5$ (correct answer)
$8$
$\sqrt{7}$
$10$