Understand Line Segment Transformation Properties - 8th Grade Math
Card 1 of 30
Identify the image of $B(-3, 5)$ after translating by $\langle -2, 1 \rangle$.
Identify the image of $B(-3, 5)$ after translating by $\langle -2, 1 \rangle$.
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$B'(-5, 6)$. Add the translation vector: $(-3+(-2), 5+1) = (-5, 6)$.
$B'(-5, 6)$. Add the translation vector: $(-3+(-2), 5+1) = (-5, 6)$.
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What must a rotation, reflection, or translation always preserve about any line segment?
What must a rotation, reflection, or translation always preserve about any line segment?
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The segment length stays the same. Rigid motions preserve all distances between points.
The segment length stays the same. Rigid motions preserve all distances between points.
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Which option is true for a line after a rigid motion: it becomes a line or it becomes a curve?
Which option is true for a line after a rigid motion: it becomes a line or it becomes a curve?
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It becomes a line. Lines map to lines under rigid motions.
It becomes a line. Lines map to lines under rigid motions.
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Identify the transformation: if points flip across a line (mirror line), what is it?
Identify the transformation: if points flip across a line (mirror line), what is it?
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A reflection. Each point maps to its mirror image across the line.
A reflection. Each point maps to its mirror image across the line.
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Which option is true for a segment after a rigid motion: it keeps length or it changes length?
Which option is true for a segment after a rigid motion: it keeps length or it changes length?
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It keeps the same length. Rigid motions preserve all distances.
It keeps the same length. Rigid motions preserve all distances.
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Which option must be true after a rigid motion: $AB = A'B'$ or $AB \ne A'B'$?
Which option must be true after a rigid motion: $AB = A'B'$ or $AB \ne A'B'$?
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$AB = A'B'$. Equal lengths show distance preservation.
$AB = A'B'$. Equal lengths show distance preservation.
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Identify whether this statement is true or false: A rigid motion can map a line to a segment.
Identify whether this statement is true or false: A rigid motion can map a line to a segment.
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False. Lines are infinite; segments are finite portions.
False. Lines are infinite; segments are finite portions.
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Identify whether this statement is true or false: A rigid motion can map a segment to a ray.
Identify whether this statement is true or false: A rigid motion can map a segment to a ray.
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False. Segments map to segments of equal length, not rays.
False. Segments map to segments of equal length, not rays.
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Find the image length: if $AB = 7$ and a rigid motion maps $A \to A'$ and $B \to B'$, what is $A'B'$?
Find the image length: if $AB = 7$ and a rigid motion maps $A \to A'$ and $B \to B'$, what is $A'B'$?
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$A'B' = 7$. Rigid motions preserve all segment lengths.
$A'B' = 7$. Rigid motions preserve all segment lengths.
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Find and correct the error: A student claims a translation changes $\overline{AB}$ from length $5$ to length $6$.
Find and correct the error: A student claims a translation changes $\overline{AB}$ from length $5$ to length $6$.
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Correct: the image length stays $5$. Translations are rigid motions that preserve length.
Correct: the image length stays $5$. Translations are rigid motions that preserve length.
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Identify the image of a segment: if $\overline{AB}$ is transformed, what is its image called?
Identify the image of a segment: if $\overline{AB}$ is transformed, what is its image called?
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The segment $\overline{A'B'}$. Prime notation indicates the transformed version.
The segment $\overline{A'B'}$. Prime notation indicates the transformed version.
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Identify the key property of rigid motions using notation: if $A \to A'$ and $B \to B'$, what is true about $\overline{AB}$ and $\overline{A'B'}$?
Identify the key property of rigid motions using notation: if $A \to A'$ and $B \to B'$, what is true about $\overline{AB}$ and $\overline{A'B'}$?
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$AB = A'B'$. Rigid motions preserve distances between all point pairs.
$AB = A'B'$. Rigid motions preserve distances between all point pairs.
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What does a line map to under any rigid motion (rotation, reflection, or translation)?
What does a line map to under any rigid motion (rotation, reflection, or translation)?
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A line. Rigid motions preserve the linear structure of lines.
A line. Rigid motions preserve the linear structure of lines.
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What happens to the length of a segment under a translation?
What happens to the length of a segment under a translation?
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The length stays the same. Translations preserve all distances between points.
The length stays the same. Translations preserve all distances between points.
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What happens to the length of a segment under a reflection?
What happens to the length of a segment under a reflection?
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The length stays the same. Reflections preserve all distances between points.
The length stays the same. Reflections preserve all distances between points.
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What happens to the length of a segment under a rotation?
What happens to the length of a segment under a rotation?
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The length stays the same. Rotations preserve all distances between points.
The length stays the same. Rotations preserve all distances between points.
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Which transformations are rigid motions: rotation, reflection, translation, dilation?
Which transformations are rigid motions: rotation, reflection, translation, dilation?
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Rotation, reflection, and translation. These three preserve distances; dilation changes them.
Rotation, reflection, and translation. These three preserve distances; dilation changes them.
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What is the name of a transformation that preserves distances and angle measures?
What is the name of a transformation that preserves distances and angle measures?
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A rigid transformation (isometry). Preserves all distances and angles between points.
A rigid transformation (isometry). Preserves all distances and angles between points.
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What is the correct term for two segments with the same length?
What is the correct term for two segments with the same length?
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Congruent segments. Same length means the segments are congruent.
Congruent segments. Same length means the segments are congruent.
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What does a line segment map to under any rigid motion (rotation, reflection, or translation)?
What does a line segment map to under any rigid motion (rotation, reflection, or translation)?
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A congruent line segment. Rigid motions preserve both shape and size.
A congruent line segment. Rigid motions preserve both shape and size.
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Identify the transformation: if every point moves the same distance in the same direction, what is it?
Identify the transformation: if every point moves the same distance in the same direction, what is it?
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A translation. All points slide the same vector distance.
A translation. All points slide the same vector distance.
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Identify the transformation: if points turn around a fixed point by a given angle, what is it?
Identify the transformation: if points turn around a fixed point by a given angle, what is it?
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A rotation. Points maintain distance from the center of rotation.
A rotation. Points maintain distance from the center of rotation.
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Identify the transformation that flips a figure across a line (the line of reflection).
Identify the transformation that flips a figure across a line (the line of reflection).
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Reflection. Each point maps to its mirror image across the line.
Reflection. Each point maps to its mirror image across the line.
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Identify the transformation that turns a figure around a fixed point by a given angle.
Identify the transformation that turns a figure around a fixed point by a given angle.
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Rotation. Points move along circular arcs around the center.
Rotation. Points move along circular arcs around the center.
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What always happens to a line segment after a rotation, reflection, or translation?
What always happens to a line segment after a rotation, reflection, or translation?
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It maps to a line segment of the same length. Rigid motions preserve distances between endpoints.
It maps to a line segment of the same length. Rigid motions preserve distances between endpoints.
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What always happens to a line after a rotation, reflection, or translation?
What always happens to a line after a rotation, reflection, or translation?
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It maps to a line. Rigid motions preserve collinearity of points.
It maps to a line. Rigid motions preserve collinearity of points.
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What does it mean to say a line segment maps to a segment of the same length under a rigid motion?
What does it mean to say a line segment maps to a segment of the same length under a rigid motion?
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The image segment is congruent to the original. Same length means equal measures: $AB = A'B'$.
The image segment is congruent to the original. Same length means equal measures: $AB = A'B'$.
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Which option describes the image of a line segment under a rigid motion: ray, segment, circle, parabola?
Which option describes the image of a line segment under a rigid motion: ray, segment, circle, parabola?
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A line segment. Rigid motions preserve shape and size.
A line segment. Rigid motions preserve shape and size.
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Which option is true for a rigid motion: it preserves length, it changes length, it scales length?
Which option is true for a rigid motion: it preserves length, it changes length, it scales length?
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It preserves length. Definition of rigid motion: distance-preserving.
It preserves length. Definition of rigid motion: distance-preserving.
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What is the relationship between perpendicular lines after a rigid motion?
What is the relationship between perpendicular lines after a rigid motion?
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Perpendicular lines map to perpendicular lines. Right angles remain right angles after rigid motion.
Perpendicular lines map to perpendicular lines. Right angles remain right angles after rigid motion.
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