Question

question 8 of 10
△abc is reflected across the x - axis and then dilated by a factor of 2 using the point (-2, 1) as the center of dilation. what is the transformation of a(3, 1)?
a. a(-6, 2)
b. a(8, -3)
c. a(6, -2)
d. a(3, -1)

Explanation:

Step1: Reflect across x - axis

When reflecting point $A(3,1)$ across the x - axis, the y - coordinate changes sign. So the new point is $A_1(3, - 1)$.

Step2: Dilate about center $(-2,1)$

First find vector from center $(-2,1)$ to $A_1(3,-1)$: $\vec{v}=(3 - (-2),-1 - 1)=(5,-2)$. Multiply by dilation factor 2: $(10,-4)$. New point $A'$: $(-2+10,1+( - 4))=(8,-3)$.

Answer:

B. $A'(8, - 3)$