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 property

For a point $(x,y)$ reflected across the vertical line $x = a$, the formula for the $x$-coordinate of the pre - image is $x = 2a - x'$, where $x'$ is the $x$-coordinate of the image. The $y$-coordinate remains the same for a reflection across a vertical line.

Step2: Identify values

The line of reflection is $x=-3$ and the $x$-coordinate of $Q'$ is $x' = 2$, and the $y$-coordinate of $Q'$ is $y'=4$.

Step3: Calculate $x$-coordinate of $Q$

Using the formula $x = 2a - x'$, substitute $a=-3$ and $x' = 2$. So $x=2\times(-3)-2=-6 - 2=-8$. The $y$-coordinate of $Q$ is the same as that of $Q'$, which is $y = 4$.

Answer:

D. $(-8,4)$