$\\overline{pq}$ is reflected across the line $x = -3$. the coordinates of the endpoints of the image of…

$\\overline{pq}$ is reflected across the line $x = -3$. the coordinates of the endpoints of the image of $\\overline{pq}$ are $p(5, 2)$ and $q(2, 4)$. what are the coordinates of $q$? \na $(1, 4)$ \nb $(-3, 4)$ \nc $(5, 4)$ \nd $(-8, 4)$

$\\overline{pq}$ is reflected across the line $x = -3$. the coordinates of the endpoints of the image of $\\overline{pq}$ are $p(5, 2)$ and $q(2, 4)$. what are the coordinates of $q$? \na $(1, 4)$ \nb $(-3, 4)$ \nc $(5, 4)$ \nd $(-8, 4)$

Answer

Answer:

D. (-8, 4)

Explanation:

Step1: Recall reflection rule for $x=k$

For a point $(x,y)$ reflected over $x=k$, the pre-image $x$-coordinate is found by $x = 2k - x'$, where $x'$ is the image $x$-coordinate. The $y$-coordinate stays the same.

Step2: Identify given values

We have $k=-3$, $x'=2$, $y'=4$.

Step3: Calculate pre-image $x$-coordinate

$$x = 2(-3) - 2 = -6 - 2 = -8$$

Step4: Keep $y$-coordinate unchanged

$y = y' = 4$

Step5: State pre-image $Q$ coordinates

The coordinates of $Q$ are $(-8, 4)$