$overline{pq}$ 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

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

Step2: Calculate x - coordinate of Q

Substitute $a=-3$ and $x' = 2$ into the formula $x = 2a-x'$. So $x=2\times(-3)-2=-6 - 2=-8$.

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. $(-8,4)$