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 new $x$-coordinate $x'$ is $x'=2a - x$. Here $a=-3$.

Step2: Let the coordinates of $Q$ be $(x,y)$.

We know the coordinates of $Q'$ are $(2,4)$. Since reflection across $x = - 3$ only changes the $x$-coordinate and the $y$-coordinate remains the same, $y = 4$.

Step3: Use the reflection formula for $x$-coordinate.

We have $2=2\times(-3)-x$. Solving for $x$:
\[

$$\begin{align*} 2&=-6 - x\\ x&=-6 - 2\\ x&=-8 \end{align*}$$

\]

Answer:

D. $(-8,4)$