ISEE Middle Level Quantitative Reasoning Flashcards: Transformations And Symmetry

What this deck covers

This deck focuses on Transformations And Symmetry, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Middle Level Quantitative Reasoning.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the transformation rule for reflecting a point $(x,y)$ across the $x$-axis?

Answer: $(x,y)\rightarrow(x,-y)$. Reflection across the x-axis negates the y-coordinate while preserving the x-coordinate to mirror the point below or above the axis.

Flashcard 2: What is the transformation rule for reflecting a point $(x,y)$ across the $y$-axis?

Answer: $(x,y)\rightarrow(-x,y)$. Reflection across the y-axis negates the x-coordinate while preserving the y-coordinate to mirror the point left or right of the axis.

Flashcard 3: What is the transformation rule for reflecting a point $(x,y)$ across the line $y=x$?

Answer: $(x,y)\rightarrow(y,x)$. Reflection across the line $y=x$ swaps the x- and y-coordinates to mirror the point over the diagonal.

Flashcard 4: What is the transformation rule for reflecting a point $(x,y)$ across the line $y=-x$?

Answer: $(x,y)\rightarrow(-y,-x)$. Reflection across the line $y=-x$ swaps the coordinates and negates both to mirror the point over the anti-diagonal.

Flashcard 5: What is the transformation rule for a $90^\circ$ counterclockwise rotation about the origin?

Answer: $(x,y)\rightarrow(-y,x)$. A $90^\circ$ counterclockwise rotation transforms the coordinates by setting new x to -y and new y to x.

Flashcard 6: What is the transformation rule for a $90^\circ$ clockwise rotation about the origin?

Answer: $(x,y)\rightarrow(y,-x)$. A $90^\circ$ clockwise rotation transforms the coordinates by setting new x to y and new y to -x.

Flashcard 7: What is the transformation rule for a $180^\circ$ rotation about the origin?

Answer: $(x,y)\rightarrow(-x,-y)$. A $180^\circ$ rotation negates both x- and y-coordinates to rotate the point halfway around the origin.

Flashcard 8: What is the transformation rule for translating a point $(x,y)$ by $(a,b)$?

Answer: $(x,y)\rightarrow(x+a,y+b)$. Translation shifts the point by adding a to the x-coordinate and b to the y-coordinate.

Flashcard 9: What is the transformation rule for dilating a point $(x,y)$ by scale factor $k$ about the origin?

Answer: $(x,y)\rightarrow(kx,ky)$. Dilation enlarges or reduces the figure by multiplying both coordinates by the scale factor k from the origin.

Flashcard 10: What is the scale factor $k$ for a dilation if a segment of length $L$ becomes length $L'$?

Answer: $k=\frac{L'}{L}$. The scale factor is the ratio of the image length to the original length under dilation.

Flashcard 11: Which transformations always preserve distance and angle measure: translation, rotation, reflection, or dilation?

Answer: Translation, rotation, and reflection. These are rigid motions that preserve congruence, maintaining distances and angles, unlike dilation which alters size.

Flashcard 12: What happens to area under a dilation with scale factor $k$ (in terms of the original area $A$)?

Answer: New area $=k^2A$. Areas scale by the square of the linear scale factor under dilation.

Flashcard 13: Identify the type of symmetry: a figure can be mapped onto itself by a reflection across a line.

Answer: Line symmetry (reflectional symmetry). This symmetry allows the figure to coincide with itself when folded along the line of reflection.

Flashcard 14: Identify the type of symmetry: a figure can be mapped onto itself by a rotation about a point.

Answer: Rotational symmetry. This symmetry allows the figure to coincide with itself after rotation by a specific angle around a center point.

Flashcard 15: What is the order of rotational symmetry if the smallest rotation that maps a figure onto itself is $120^\circ$?

Answer: $3$. The order is $360^\circ$ divided by the smallest rotation angle that maps the figure onto itself.

Flashcard 16: What is the smallest positive rotation angle if a figure has rotational symmetry of order $5$?

Answer: $72^\circ$. The smallest angle is $360^\circ$ divided by the order of rotational symmetry.

Flashcard 17: Find the image of point $A(3,-5)$ after reflection across the $x$-axis.

Answer: $(3,5)$. Apply the x-axis reflection rule by negating the y-coordinate of (3,-5).

Flashcard 18: Find the image of point $B(-4,2)$ after reflection across the $y$-axis.

Answer: $(4,2)$. Apply the y-axis reflection rule by negating the x-coordinate of (-4,2).

Flashcard 19: Find the image of point $C(7,-1)$ after reflection across the line $y=x$.

Answer: $(-1,7)$. Apply the $y=x$ reflection rule by swapping the coordinates of (7,-1).

Flashcard 20: Find the image of point $D(2,9)$ after a $90^\circ$ counterclockwise rotation about the origin.

Answer: $(-9,2)$. Apply the $90^\circ$ counterclockwise rotation rule to (2,9) by setting new x to -9 and new y to 2.

Flashcard 21: Find the image of point $E(-6,1)$ after a $180^\circ$ rotation about the origin.

Answer: $(6,-1)$. Apply the $180^\circ$ rotation rule to (-6,1) by negating both coordinates.

Flashcard 22: Find the image of point $F(1,-3)$ after translation by $(4,-2)$.

Answer: $(5,-5)$. Apply the translation by adding 4 to x and -2 to y of (1,-3).

Flashcard 23: A segment of length $8$ is dilated by scale factor $\frac{3}{2}$. What is the new length?

Answer: $12$. The new length is the original length multiplied by the scale factor $\frac{3}{2}$.

Flashcard 24: A rectangle has area $10$. It is dilated by scale factor $3$. What is the new area?

Answer: $90$. The new area is the original area multiplied by the square of the scale factor 3.

Flashcard 25: A figure has line symmetry about the $y$-axis. If it contains $(5,-2)$, what reflected point must it contain?

Answer: $(-5,-2)$. Symmetry about the y-axis requires the point symmetric to (5,-2) by negating its x-coordinate.