8th Grade Math Flashcards: Describe Transformation Effects Using Coordinates

What this deck covers

This deck focuses on Describe Transformation Effects Using Coordinates, 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: Identify the image of $P(-3,4)$ after translation by $(5,-2)$.

Answer: $(2,2)$. Apply translation: $(-3+5, 4+(-2)) = (2,2)$.

Flashcard 2: Which transformations always preserve distance (are rigid motions): translation, rotation, reflection, dilation?

Answer: Translation, rotation, and reflection. Only dilation changes distances; the others preserve them.

Flashcard 3: What is the coordinate rule for a $180^\circ$ rotation about the origin?

Answer: $(x,y)\rightarrow(-x,-y)$. Negate both coordinates for half-turn around origin.

Flashcard 4: What is the coordinate rule for a $90^\circ$ clockwise rotation about the origin?

Answer: $(x,y)\rightarrow(y,-x)$. Swap coordinates and negate new $y$ for $90°$ CW rotation.

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

Answer: $(x,y)\rightarrow(-y,x)$. Swap coordinates and negate new $x$ for $90°$ CCW rotation.

Flashcard 6: Identify the image of $(-2,5)$ after reflection across the line $y=x$.

Answer: $(5,-2)$. Swap coordinates: $(x,y)$ becomes $(y,x)$ across $y=x$.

Flashcard 7: Identify the image of $(4,-1)$ after reflection across the $x$-axis.

Answer: $(4,1)$. Negate $y$-coordinate: $-1$ becomes $1$, $x$ stays $4$.

Flashcard 8: What is the coordinate rule for reflecting a point $(x,y)$ across the line $y=-x$?

Answer: $(x,y)\rightarrow(-y,-x)$. Swap and negate both coordinates for reflection across $y=-x$.

Flashcard 9: Identify the image of $(2,7)$ after a $90^\circ$ counterclockwise rotation about the origin.

Answer: $(-7,2)$. Apply rule: $(2,7) → (-7,2)$ by swapping and negating new $x$.

Flashcard 10: Identify the image of $(-6,3)$ after a $180^\circ$ rotation about the origin.

Answer: $(6,-3)$. Negate both: $(-6,3) → (6,-3)$ for $180°$ rotation.

Flashcard 11: What is the coordinate rule for dilating a point $(x,y)$ by scale factor $k$ about the origin?

Answer: $(x,y)\rightarrow(kx,ky)$. Multiply both coordinates by scale factor $k$.

Flashcard 12: Identify the image of $(8,-4)$ after dilation about the origin with scale factor $\frac{1}{2}$.

Answer: $(4,-2)$. Multiply by rac{1}{2}: $(8,-4) → (4,-2)$.

Flashcard 13: What is always true about side lengths after a dilation with scale factor $k$?

Answer: Each length is multiplied by $|k|$. Dilation scales all distances by the absolute value of $k$.

Flashcard 14: What happens to angle measures under translations, rotations, reflections, and dilations?

Answer: Angles stay equal for all four transformations. All four transformations preserve angle measures.

Flashcard 15: What is the coordinate rule for reflecting a point $(x,y)$ across the line $y=x$?

Answer: $(x,y)\rightarrow(y,x)$. Swap coordinates to reflect across the diagonal line $y=x$.

Flashcard 16: What is the coordinate rule for reflecting a point $(x,y)$ across the $y$-axis?

Answer: $(x,y)\rightarrow(-x,y)$. Negate the $x$-coordinate to flip across the vertical axis.

Flashcard 17: What is the coordinate rule for reflecting a point $(x,y)$ across the $x$-axis?

Answer: $(x,y)\rightarrow(x,-y)$. Negate the $y$-coordinate to flip across the horizontal axis.

Flashcard 18: Identify the image of the point $(3,-2)$ after the translation $(x,y)\rightarrow(x-5,y+4)$.

Answer: $(-2,2)$. Apply the rule: $3-5=-2$ for $x$, $-2+4=2$ for $y$.

Flashcard 19: What is the coordinate rule for translating a point $(x,y)$ by $(a,b)$?

Answer: $(x,y)\rightarrow(x+a,y+b)$. Add $a$ to $x$-coordinate and $b$ to $y$-coordinate to shift the point.

Flashcard 20: What is the coordinate rule for translating a point by $(a,b)$?

Answer: $(x,y)\rightarrow(x+a,y+b)$. Add $a$ to $x$-coordinate and $b$ to $y$-coordinate to shift the point.

Flashcard 21: Identify the scale factor $k$ if $P(2,3)$ dilates about the origin to $P'(6,9)$.

Answer: $k=3$. Since $(2 cdot 3, 3 cdot 3) = (6,9)$, the scale factor is $3$.

Flashcard 22: Identify the image of $P(7,-3)$ after a $180^\circ$ rotation about the origin.

Answer: $(-7,3)$. Negate both: $(7,-3) \rightarrow (-7,3)$

Flashcard 23: Identify the image of $P(5,-2)$ after dilation about the origin with $k=-3$.

Answer: $(-15,6)$. Multiply by $-3$: $(5 \cdot (-3), -2 \cdot (-3)) = (-15,6)$.

Flashcard 24: What is the coordinate rule for reflecting a point across the $x$-axis?

Answer: $(x,y)\rightarrow(x,-y)$. Negate the $y$-coordinate while keeping $x$ unchanged.

Flashcard 25: What is the coordinate rule for reflecting a point across the $y$-axis?

Answer: $(x,y)\rightarrow(-x,y)$. Negate the $x$-coordinate while keeping $y$ unchanged.

Flashcard 26: What is the coordinate rule for reflecting a point across the line $y=x$?

Answer: $(x,y)\rightarrow(y,x)$. Swap the $x$ and $y$ coordinates.

Flashcard 27: Identify the image of $P(6,-1)$ after reflection across the $x$-axis.

Answer: $(6,1)$. Reflecting across $x$-axis negates $y$: $(6,-1) ightarrow (6,1)$.

Flashcard 28: Identify the image of $P(-2,5)$ after reflection across the $y$-axis.

Answer: $(2,5)$. Reflecting across $y$-axis negates $x$: $(-2,5) ightarrow (2,5)$.

Flashcard 29: Identify the image of $P(3,-7)$ after reflection across the line $y=x$.

Answer: $(-7,3)$. Swap coordinates: $(3,-7) ightarrow (-7,3)$.

Flashcard 30: Identify the image of $P(2,-5)$ after a $90^\circ$ counterclockwise rotation about the origin.

Answer: $(5,2)$. Apply rule: $(2,-5) ightarrow (-(-5),2) = (5,2)$.