Question

write the coordinates of the vertices after a reflection over the line y = x.

Explanation:

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

• Assume from the graph that the coordinates of point \(E\) are \((- 9,8)\), the coordinates of point \(F\) are \((-3,8)\), and the coordinates of point \(G\) are \((-6,4)\).
• The rule for reflecting a point \((x,y)\) over the line \(y = x\) is \((x,y)\to(y,x)\).

1. Then, apply the reflection - rule to each vertex:

• For point \(E(-9,8)\):
• When we reflect it over the line \(y = x\), using the rule \((x,y)\to(y,x)\), the new coordinates of \(E'\) are \((8,-9)\).
• For point \(F(-3,8)\):
• Applying the rule \((x,y)\to(y,x)\), the new coordinates of \(F'\) are \((8,-3)\).
• For point \(G(-6,4)\):
• Applying the rule \((x,y)\to(y,x)\), the new coordinates of \(G'\) are \((4,-6)\).

Step1: Identify original coordinates

Assume \(E(-9,8)\), \(F(-3,8)\), \(G(-6,4)\)

Step2: Apply reflection rule to \(E\)

\((-9,8)\to(8,-9)\)

Step3: Apply reflection rule to \(F\)

\((-3,8)\to(8,-3)\)

Step4: Apply reflection rule to \(G\)

\((-6,4)\to(4,-6)\)

Answer:

The coordinates of the vertices after reflection are \(E'(8,-9)\), \(F'(8,-3)\), \(G'(4,-6)\)