Question

which of the following are vertices of the image of $\triangle xyz$ after a reflection in the $y$-axis and a dilation with a scale factor of 2? select all that apply.
a $(-8,4)$
b $(2,-4)$
c $(-10,8)$
d $(8,4)$
e $(10,8)$

Explanation:

Step1: Identify original vertices

From the grid:
$X(-5, -4)$, $Y(4, 2)$, $Z(1, 4)$

Step2: Reflect over y-axis

Rule: $(x,y)\to(-x,y)$
$X': (5, -4)$, $Y': (-4, 2)$, $Z': (-1, 4)$

Step3: Dilate by scale factor 2

Rule: $(x,y)\to(2x,2y)$
$X'': (5\times2, -4\times2)=(10, -8)$
$Y'': (-4\times2, 2\times2)=(-8, 4)$
$Z'': (-1\times2, 4\times2)=(-2, 8)$

Step4: Match with options

Compare results to given choices.

Answer:

A. $(-8,4)$