Question

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

Explanation:

Step1: Recall the rule for reflection over the y - axis

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

Step2: Find the coordinates of \(A\)

The original coordinates of \(A\) are \((- 10,-9)\). Using the reflection rule \((x,y)\to(-x,y)\), for \(A(-10,-9)\), we have \(x=-10\) and \(y = - 9\). Then \(A'=(10,-9)\) since \(-x=-(-10) = 10\) and \(y\) remains \(-9\).

Step3: Find the coordinates of \(B\)

The original coordinates of \(B\) are \((0,-9)\). Using the reflection rule \((x,y)\to(-x,y)\), for \(B(0,-9)\), we have \(x = 0\) and \(y=-9\). Then \(B'=(0,-9)\) since \(-x=-0 = 0\) and \(y\) remains \(-9\).

Step4: Find the coordinates of \(C\)

The original coordinates of \(C\) are \((0,-1)\). Using the reflection rule \((x,y)\to(-x,y)\), for \(C(0,-1)\), we have \(x = 0\) and \(y=-1\). Then \(C'=(0,-1)\) since \(-x=-0 = 0\) and \(y\) remains \(-1\).

Step5: Find the coordinates of \(D\)

The original coordinates of \(D\) are \((-10,-1)\). Using the reflection rule \((x,y)\to(-x,y)\), for \(D(-10,-1)\), we have \(x=-10\) and \(y = - 1\). Then \(D'=(10,-1)\) since \(-x=-(-10)=10\) and \(y\) remains \(-1\).

Answer:

\(A'(10,-9)\), \(B'(0,-9)\), \(C'(0,-1)\), \(D'(10,-1)\)