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

The line of reflection $x = - 3$ is a vertical line. For a point $(x,y)$ reflected across the vertical line $x = a$, the formula for the $x$-coordinate of the pre - image given the image is $x_0=2a - x_1$, where $x_1$ is the $x$-coordinate of the image and $x_0$ is the $x$-coordinate of the pre - image, and the $y$-coordinate remains the same. Here $a=-3$ and the image point $Q'(x_1,y_1)=(2,4)$.

Step2: Calculate $x$-coordinate of $Q$

Using the formula $x_0 = 2a-x_1$, substitute $a=-3$ and $x_1 = 2$. So $x_0=2\times(-3)-2=-6 - 2=-8$. The $y$-coordinate of $Q$ is the same as the $y$-coordinate of $Q'$, which is $y = 4$.

Answer:

D. $(-8,4)$