Question

The vertices of a triangle are P(–2, –3), Q(–4, –2), and R(4, 8). What are the vertices of the image reflected across the y-axis?

P(–2, 3), Q(–4, 2), and R(4, -8)
P(2, –3), Q(4, –2), and R(-4, 8)
P(–2, –3), Q(–4, –2), and R(4, 8)
P(-3, -2), Q(-2, -4), and R(8, 4)

Answer 1

`\huge\boxed{P(2;\ -3);\ Q(4;\ -2)\ \text{and}\ R(-4;\ 8)}`

Explanation:

`A(x;\ y)\xrightarrow{S_(OY)}A'(-x;\ y)\\\\\text{The abscissa changes to the opposite:}\ x\to -x\\\\\text{Therefore}\\\\P(-2;\ -3)\xrightarrow{S_(OY)}P'(2;\ -3)\\\\Q(-4;\ -2)\xrightarrow{S_(OY)}Q'(4;\ -2)\\\\R(4;\ 8)\xrightarrow{S_(OY)}R'(-4;\ 8)`