Question

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

c(),
d(),
e(),
f()

Explanation:

Step1: Recall the reflection rule

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

Step2: Find coordinates of \(C\)

The coordinate of \(C\) is \((-7,-8)\). Using the reflection rule \((x,y)\to(-x,y)\), for \(C(-7,-8)\), we have \(x = - 7\), \(y=-8\). Then \(C'\) has \(x\)-coordinate \(-(-7)=7\) and \(y\)-coordinate \(-8\). So \(C'(7,-8)\).

Step3: Find coordinates of \(D\)

The coordinate of \(D\) is \((-3,-8)\). Using the reflection rule \((x,y)\to(-x,y)\), for \(D(-3,-8)\), we have \(x=-3\), \(y = - 8\). Then \(D'\) has \(x\)-coordinate \(-(-3)=3\) and \(y\)-coordinate \(-8\). So \(D'(3,-8)\).

Step4: Find coordinates of \(E\)

The coordinate of \(E\) is \((-3,-1)\). Using the reflection rule \((x,y)\to(-x,y)\), for \(E(-3,-1)\), we have \(x=-3\), \(y=-1\). Then \(E'\) has \(x\)-coordinate \(-(-3)=3\) and \(y\)-coordinate \(-1\). So \(E'(3,-1)\).

Step5: Find coordinates of \(F\)

The coordinate of \(F\) is \((-7,-1)\). Using the reflection rule \((x,y)\to(-x,y)\), for \(F(-7,-1)\), we have \(x=-7\), \(y=-1\). Then \(F'\) has \(x\)-coordinate \(-(-7)=7\) and \(y\)-coordinate \(-1\). So \(F'(7,-1)\).

Answer:

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