8th Grade Math Flashcards: Understand Similarity Through Transformations

What this deck covers

This deck focuses on Understand Similarity Through Transformations, giving you a quick way to review the definitions, rules, and examples that matter most for 8th Grade Math.

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 image of point $(4,-6)$ after dilation about the origin with $k=\frac{1}{2}$?

Answer: $(2,-3)$. Apply dilation rule: $(4 × \frac{1}{2}, -6 × \frac{1}{2}) = (2, -3)$

Flashcard 2: What is the definition of scale factor in a dilation?

Answer: The ratio rac{ ext{image length}}{ ext{preimage length}}. Compares new length to original length after dilation.

Flashcard 3: What is true about side lengths in similar figures with scale factor $k$?

Answer: Corresponding side lengths have ratio $k$. Dilation multiplies all lengths by the scale factor.

Flashcard 4: Which option best describes a valid similarity sequence from figure $A$ to $B$ when $B$ is a rotated and enlarged copy?

Answer: Rotate, then dilate (translation may be included to reposition). Order matters: rotate first to align, then scale up.

Flashcard 5: What is the image of point $(2,7)$ after a $90^\circ$ counterclockwise rotation about the origin?

Answer: $(-7,2)$. Apply rotation rule: $(2, 7) → (-7, 2)$.

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

Answer: $(x,y)\rightarrow(-y,x)$. 90° CCW rotation swaps coordinates and negates new $x$.

Flashcard 7: What is the coordinate rule for a reflection across the $y$-axis?

Answer: $(x,y)\rightarrow(-x,y)$. Reflection across $y$-axis negates the $x$-coordinate.

Flashcard 8: What is the coordinate rule for a reflection across the $x$-axis?

Answer: $(x,y)\rightarrow(x,-y)$. Reflection across $x$-axis negates the $y$-coordinate.

Flashcard 9: What is the image of point $(3,-1)$ after a translation by $(5,4)$?

Answer: $(8,3)$. Add translation vector: $(3+5, -1+4) = (8, 3)$.

Flashcard 10: What is the coordinate rule for a translation by $(a,b)$?

Answer: $(x,y)\rightarrow(x+a,y+b)$. Add translation vector to each coordinate.

Flashcard 11: What is the image of point $(-2,5)$ after dilation about the origin with $k=3$?

Answer: $(-6,15)$. Apply dilation rule: $(-2×3, 5×3) = (-6, 15)$.

Flashcard 12: What is the coordinate rule for a dilation about the origin with scale factor $k$?

Answer: $(x,y)\rightarrow(kx,ky)$. Each coordinate is multiplied by the scale factor.

Flashcard 13: Identify the missing original side: if k=rac{3}{4} and the image side is $9$, what was the original side?

Answer: $12$. Divide image by scale factor: 9 ÷ rac{3}{4} = 12.

Flashcard 14: Identify the missing side: if $k=2$ and an original side is $7$, what is the image side length?

Answer: $14$. Multiply original length by scale factor: $7 × 2 = 14$.

Flashcard 15: What is the scale factor from a figure with side $10$ to a similar figure with corresponding side $4$?

Answer: k=rac{4}{10}=rac{2}{5}. Scale factor = image length ÷ original length.

Flashcard 16: What is the scale factor from a figure with side $6$ to a similar figure with corresponding side $9$?

Answer: k=rac{9}{6}=rac{3}{2}. Scale factor = image length ÷ original length.

Flashcard 17: What is true about angle measures in similar figures after transformations and dilation?

Answer: All corresponding angles are equal. Dilations and rigid motions preserve angle measures.

Flashcard 18: What does a dilation with scale factor $k$ do to all lengths in a figure?

Answer: It multiplies every length by $k$. Dilation scales all distances from center by the same factor.

Flashcard 19: Which transformations are rigid motions (do not change size): rotation, reflection, translation, dilation?

Answer: Rotation, reflection, and translation. These preserve distances and angles; dilation changes size.

Flashcard 20: What does it mean for two $2$-D figures to be similar using transformations?

Answer: One can be mapped to the other by rigid motions and a dilation. Rigid motions preserve shape; dilation changes size proportionally.

Flashcard 21: What is the image of $Q(-4,1)$ after a $90^\circ$ counterclockwise rotation about the origin?

Answer: $Q'(-1,-4)$. 90° CCW rotation: $(x,y) \rightarrow (-y,x)$.

Flashcard 22: Which sequence maps $A(0,0)$ to $A'(4,-1)$ using one rigid motion?

Answer: Translate right $4$ and down $1$. Add 4 to x-coordinate and subtract 1 from y-coordinate.

Flashcard 23: Identify whether rectangles with sides $3,5$ and $6,10$ are similar.

Answer: Yes, because $\frac{6}{3}=\frac{10}{5}=2$. Both ratios equal 2, so sides are proportional.

Flashcard 24: Identify whether the figures are similar if angle measures are $40^\circ,60^\circ,80^\circ$ and $40^\circ,60^\circ,80^\circ$.

Answer: Yes, the angles match (AAA similarity). Same angles guarantee similarity for triangles.

Flashcard 25: What is the original length if the image length is $14$ under dilation with $k=2$?

Answer: $7$. Divide image length by scale factor: $14 \div 2 = 7$.

Flashcard 26: What is the image length after dilation with $k=\frac{3}{2}$ of a segment of length $8$?

Answer: $12$. Multiply original length by scale factor: $8 \times \frac{3}{2} = 12$.

Flashcard 27: Identify the scale factor from side lengths $18$ (original) and $12$ (image).

Answer: $k=\frac{12}{18}=\frac{2}{3}$. Divide image length by original length: $\frac{12}{18}=\frac{2}{3}$.

Flashcard 28: Identify the scale factor from side lengths $6$ (original) and $15$ (image).

Answer: $k=\frac{15}{6}=\frac{5}{2}$. Divide image length by original length: $\frac{15}{6}=\frac{5}{2}$.

Flashcard 29: Which option describes a valid similarity transformation sequence?

Answer: Rigid motions followed by a dilation (in any order). Combines shape-preserving moves with size change.

Flashcard 30: What does a dilation with scale factor $0<k<1$ do to a figure?

Answer: It produces a reduction (smaller similar image). Multiplying by a fraction less than 1 shrinks the figure.