Question

write the coordinates of the vertices after a reflection over the y - axis.

Explanation:

Step1: Recall the reflection rule over the y - axis

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\).

Step2: Find the coordinates of \(C\)

The coordinates of \(C\) are \((-7,-8)\). Using the reflection rule \((x,y)\to(-x,y)\), for \(C(-7,-8)\), we have \(x = - 7\) and \(y=-8\). Then \(C'=(7,-8)\) since \(-x=-(-7) = 7\) and \(y\) remains \(-8\).

Step3: Find the coordinates of \(D\)

The coordinates of \(D\) are \((-3,-8)\). Using the reflection rule \((x,y)\to(-x,y)\), for \(D(-3,-8)\), we have \(x=-3\) and \(y = - 8\). Then \(D'=(3,-8)\) since \(-x=-(-3)=3\) and \(y\) remains \(-8\).

Step4: Find the coordinates of \(E\)

The coordinates of \(E\) are \((-3,-1)\). Using the reflection rule \((x,y)\to(-x,y)\), for \(E(-3,-1)\), we have \(x=-3\) and \(y=-1\). Then \(E'=(3,-1)\) since \(-x=-(-3) = 3\) and \(y\) remains \(-1\).

Step5: Find the coordinates of \(F\)

The coordinates of \(F\) are \((-7,-1)\). Using the reflection rule \((x,y)\to(-x,y)\), for \(F(-7,-1)\), we have \(x=-7\) and \(y=-1\). Then \(F'=(7,-1)\) since \(-x=-(-7)=7\) and \(y\) remains \(-1\).

Answer:

\(C'(7,-8)\), \(D'(3,-8)\), \(E'(3,-1)\), \(F'(7,-1)\)