Question

write the coordinates of the vertices after a reflection over the line x = 2.

Explanation:

Step1: Recall reflection formula

For a point $(x,y)$ reflected over the line $x = a$, the new $x$-coordinate is $2a - x$ and the $y$-coordinate remains the same. Here $a = 2$.

Step2: Find coordinates of point C

The coordinates of point C are $(5,-7)$. Using the formula, the new $x$-coordinate is $2\times2 - 5=-1$, and the $y$-coordinate remains $-7$. So the new coordinates of C are $(-1,-7)$.

Step3: Find coordinates of point D

The coordinates of point D are $(6,0)$. Using the formula, the new $x$-coordinate is $2\times2 - 6=-2$, and the $y$-coordinate remains $0$. So the new coordinates of D are $(-2,0)$.

Step4: Find coordinates of point E

The coordinates of point E are $(8,0)$. Using the formula, the new $x$-coordinate is $2\times2 - 8=-4$, and the $y$-coordinate remains $0$. So the new coordinates of E are $(-4,0)$.

Step5: Find coordinates of point F

The coordinates of point F are $(7,-7)$. Using the formula, the new $x$-coordinate is $2\times2 - 7=-3$, and the $y$-coordinate remains $-7$. So the new coordinates of F are $(-3,-7)$.

Answer:

C: $(-1,-7)$, D: $(-2,0)$, E: $(-4,0)$, F: $(-3,-7)$