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 line $x = a$, the formula for the x - coordinate of the pre - image is $x_{pre}=2a - x_{image}$. Here $a=-3$ and the x - coordinate of $Q'$ is $x_{Q'}=2$.

Step2: Calculate x - coordinate of Q

Using the formula $x_{Q}=2\times(-3)-2=-6 - 2=-8$.

Step3: Note y - coordinate property

When reflecting across a vertical line, the y - coordinate of a point and its image remains the same. The y - coordinate of $Q'$ is $y_{Q'}=4$, so $y_{Q}=4$.

Answer:

D. $(-8,4)$