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 $x_0=2a - x_1$, where $x_1$ is the x - coordinate of the image and $a$ is the x - coordinate of the line of reflection. Here, $a=-3$ and for point $Q'$, $x_1 = 2$.

Step2: Calculate x - coordinate of Q

Using the formula $x_0=2\times(-3)-2=-6 - 2=-8$.

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. $(-8,4)$