Question

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

Explanation:

Step1: Recall the reflection rule

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

Step2: Find coordinates of \(T\)

The coordinates of \(T\) are \((4,1)\). After reflection over \(y = x\), using the rule \((x,y)\to(y,x)\), we get \((1,4)\).

Step3: Find coordinates of \(S\)

The coordinates of \(S\) are \((4,-9)\). After reflection over \(y = x\), using the rule \((x,y)\to(y,x)\), we get \((-9,4)\).

Step4: Find coordinates of \(U\)

The coordinates of \(U\) are \((8,-9)\). After reflection over \(y = x\), using the rule \((x,y)\to(y,x)\), we get \((-9,8)\).

Answer:

\(T'(1,4)\), \(S'(-9,4)\), \(U'(-9,8)\)