Question

pq is reflected across the line x = - 3. the coordinates of the endpoints of the image of pq are p(5,2) and q(2,4). what are the coordinates of q? a (1,4) b (-3,4) c (5,4) d (-8,4)

Explanation:

Step1: Recall reflection rule for x - coordinate

When reflecting a point across the vertical line $x = a$, the formula for the x - coordinate of the pre - image $(x)$ given the x - coordinate of the image $(x')$ is $x=2a - x'$. Here $a=-3$ and for point $Q'$ with $x' = 2$.

Step2: Calculate x - coordinate of Q

Substitute $a=-3$ and $x' = 2$ into the formula $x = 2a-x'$. So $x=2\times(-3)-2=-6 - 2=-8$.

Step3: Note y - coordinate remains the same

Since reflection across a vertical line does not change the y - coordinate, and the y - coordinate of $Q'$ is 4, the y - coordinate of $Q$ is also 4.

Answer:

D. $(-8,4)$