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 formula for x - coordinate

For a point $(x,y)$ reflected across the vertical line $x = a$, the formula for the x - coordinate of the pre - image is $x_{pre - image}=2a - x_{image}$. Here $a=-3$ and for point $Q'$ with $x_{image}=2$.

Step2: Calculate x - coordinate of Q

Substitute $a = - 3$ and $x_{image}=2$ into the formula $x_{pre - image}=2a - x_{image}$. So $x_{Q}=2\times(-3)-2=-6 - 2=-8$.

Step3: Note y - coordinate property

When reflecting across a vertical line, the y - coordinate of a point and its image remains the same. Since the y - coordinate of $Q'$ is 4, the y - coordinate of $Q$ is also 4.

Answer:

D. $(-8,4)$