Question

pq is reflected across the line x = - 3. the coordinates of the endpoints of the image of pq are p(8,2) and q(2,4). what are the coordinates of q?

Explanation:

Step1: Recall reflection formula for x - coordinate

For a point $(x,y)$ reflected across the line $x = a$, the formula for the new $x$-coordinate $x'$ is $x'=2a - x$. Here $a=-3$ and $x' = 2$ (for point $Q'$).

Step2: Solve for original x - coordinate of Q

Substitute into the formula $2=2\times(-3)-x$. Then $2=-6 - x$. Add $x$ to both sides: $x + 2=-6$. Subtract 2 from both sides: $x=-8$.
The $y$-coordinate remains the same in a reflection across a vertical line. Since the $y$-coordinate of $Q'$ is 4, the $y$-coordinate of $Q$ is also 4.

Answer:

D. $(-8,4)$