Question

question 2 (5 points)
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triangle xyz has vertices x(2,4), y(3,4) and z(3,8). suppose you reflect this across the y - axis, then dilate it with a scale factor of 2 with the origin as the center of dilation. what are the coordinates of the resulting triangle xyz?
a) x(2, - 4), y(3, - 4), z(3, - 8)
b) x(- 2,4), y(- 3,4), z(- 3,8)
c) x(4, - 8), y(6, - 8), z(6, - 16)
d) x(- 4,8), y(- 6,8), z(- 6,16)
question 3 (5 points)
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identify the algebraic description that maps a point (- 1,5) onto another point (6, - 3).
a) (x, y) → (x + 7, y - 8)
b) (x, y) → (x - 7, y - 8)
c) (x, y) → (x - 8, y + 7)
d) (x, y) → (x - 8, y - 7)

Explanation:

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Question 2 Steps:

Step1: Reflect over y-axis

For a point $(x,y)$, reflection over y-axis gives $(-x,y)$.

• $X(2,4) \to X'(-2,4)$
• $Y(3,4) \to Y'(-3,4)$
• $Z(3,8) \to Z'(-3,8)$

Step2: Dilate by scale factor 2

For a point $(x,y)$, dilation by scale factor $k=2$ from origin gives $(2x,2y)$.

• $X'(-2,4) \to X''(2\times(-2), 2\times4)=(-4,8)$
• $Y'(-3,4) \to Y''(2\times(-3), 2\times4)=(-6,8)$
• $Z'(-3,8) \to Z''(2\times(-3), 2\times8)=(-6,16)$

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Question 3 Steps:

Step1: Calculate x-change

Find difference in x-coordinates: $6 - (-1) = 7$. So $x$ becomes $x+7$.

Step2: Calculate y-change

Find difference in y-coordinates: $-3 - 5 = -8$. So $y$ becomes $y-8$.

Step3: Form transformation

Combine changes: $(x,y) \to (x+7, y-8)$

Answer:

Question 2:

D) $X''(-4,8), Y''(-6,8), Z''(-6,16)$

Question 3:

A) $(x, y) \to (x+7, y-8)$