Question

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

Explanation:

1. First, identify the original coordinates of the vertices:

• Assume the coordinates of point \(P\) are \((-9,3)\), the coordinates of point \(Q\) are \((-2,3)\), and the coordinates of point \(R\) are \((-9,9)\).
• The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\).

1. Calculate the new coordinates of point \(P\):

• For point \(P(-9,3)\), when reflected over the \(y\) - axis, we change the sign of the \(x\) - coordinate.
• Using the rule \((x,y)\to(-x,y)\), for \(P(-9,3)\), the new \(x\) - coordinate is \(-(-9)=9\) and the \(y\) - coordinate remains \(3\). So, \(P'=(9,3)\).

1. Calculate the new coordinates of point \(Q\):

• For point \(Q(-2,3)\), when reflected over the \(y\) - axis, using the rule \((x,y)\to(-x,y)\), the new \(x\) - coordinate is \(-(-2) = 2\) and the \(y\) - coordinate remains \(3\). So, \(Q'=(2,3)\).

1. Calculate the new coordinates of point \(R\):

• For point \(R(-9,9)\), when reflected over the \(y\) - axis, using the rule \((x,y)\to(-x,y)\), the new \(x\) - coordinate is \(-(-9)=9\) and the \(y\) - coordinate remains \(9\). So, \(R'=(9,9)\).

Step1: Identify reflection rule

The rule for \(y\) - axis reflection is \((x,y)\to(-x,y)\).

Step2: Apply rule to point \(P\)

Given \(P(-9,3)\), new \(x = -(-9)=9\), \(y = 3\), so \(P'=(9,3)\).

Step3: Apply rule to point \(Q\)

Given \(Q(-2,3)\), new \(x=-(-2) = 2\), \(y = 3\), so \(Q'=(2,3)\).

Step4: Apply rule to point \(R\)

Given \(R(-9,9)\), new \(x=-(-9)=9\), \(y = 9\), so \(R'=(9,9)\).

Answer:

\(P'(9,3)\), \(Q'(2,3)\), \(R'(9,9)\)