Question

1. the vertices for triangle abc are (-2,3), (2,-2) and (6,-2). the triangle will be reflected across the line y = -5. where will triangle abc be after being reflected, please draw and provide each coordinate pair: a (_); b (_); c (___).

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ across the line $y = k$ is $(x,2k - y)$. Here $k=-5$.

Step2: Calculate coordinates of A'

For point $A(-2,3)$, using the rule $x=-2$ and $y = 3$. Then $y'=2\times(-5)-3=-10 - 3=-13$. So $A'(-2,-13)$.

Step3: Calculate coordinates of B'

For point $B(2,-2)$, $x = 2$ and $y=-2$. Then $y'=2\times(-5)-(-2)=-10 + 2=-8$. So $B'(2,-8)$.

Step4: Calculate coordinates of C'

For point $C(6,-2)$, $x = 6$ and $y=-2$. Then $y'=2\times(-5)-(-2)=-10 + 2=-8$. So $C'(6,-8)$.

Answer:

$A'(-2,-13)$; $B'(2,-8)$; $C'(6,-8)$