Question

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

Explanation:

1. Recall the rule for reflection over the line \(y = x\):

• The rule for reflecting a point \((x,y)\) over the line \(y=x\) is \((x,y)\to(y,x)\).

1. Identify the coordinates of the original vertices:

• Assume the coordinates of point \(A\) are \((- 2,-8)\), point \(B\) are \((2,-8)\), point \(C\) are \((6,-6)\) and point \(D\) are \((2,-6)\).

1. Apply the reflection - rule to each vertex:

• For point \(A(-2,-8)\):
• After reflection over \(y = x\), the new coordinates \(A'\) are \((-8,-2)\) since we swap the \(x\) and \(y\) values.
• For point \(B(2,-8)\):
• After reflection over \(y = x\), the new coordinates \(B'\) are \((-8,2)\).
• For point \(C(6,-6)\):
• After reflection over \(y = x\), the new coordinates \(C'\) are \((-6,6)\).
• For point \(D(2,-6)\):
• After reflection over \(y = x\), the new coordinates \(D'\) are \((-6,2)\).

Answer:

The coordinates of the vertices after reflection over the line \(y = x\) are \(A'(-8,-2)\), \(B'(-8,2)\), \(C'(-6,6)\), \(D'(-6,2)\)