Question

write the coordinates of the vertices after a reflection over the y-axis.
b((
c(
d(

Explanation:

Step1: Recall the reflection rule over the y - axis

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

Step2: Find the coordinates of \(B\)

From the graph, the coordinates of \(B\) are \((- 2,1)\). Using the reflection rule \((x,y)\to(-x,y)\), for \(B(-2,1)\), we have \(x=-2\) and \(y = 1\). Then \(B'=(2,1)\) since \(-x=-(-2) = 2\) and \(y\) remains \(1\).

Step3: Find the coordinates of \(C\)

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

Step4: Find the coordinates of \(D\)

From the graph, the coordinates of \(D\) are \((-6,0)\). Using the reflection rule \((x,y)\to(-x,y)\), we have \(x=-6\) and \(y = 0\). Then \(D'=(6,0)\) since \(-x=-(-6)=6\) and \(y\) remains \(0\).

Answer:

\(B'(2,1)\), \(C'(3,8)\), \(D'(6,0)\)