Question

suppose line h is the line with equation y = - 1. given a(7, - 4), b(6,4), and c(- 1, - 6). what are the coordinates of the vertices of △abc for the reflection?
a
(type an ordered pair.)

Explanation:

Step1: Recall reflection formula

For reflection over the line $y = k$, if a point is $(x,y)$, its image is $(x,2k - y)$. Here $k=-1$.

Step2: Find $A'$

For point $A(7,-4)$, using the formula, $x = 7$, $y=-4$, then $y'=2\times(-1)-(-4)=-2 + 4=2$. So $A'=(7,2)$.

Step3: Find $B'$

For point $B(6,4)$, $x = 6$, $y = 4$, then $y'=2\times(-1)-4=-2-4=-6$. So $B'=(6,-6)$.

Step4: Find $C'$

For point $C(-1,-6)$, $x=-1$, $y=-6$, then $y'=2\times(-1)-(-6)=-2 + 6 = 4$. So $C'=(-1,4)$.

Answer:

$A'(7,2)$
$B'(6,-6)$
$C'(-1,4)$