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 \(R\)

The coordinates of \(R\) are \((- 3,-4)\). Using the reflection rule \((x,y)\to(y,x)\), we get \((-4,-3)\).

Step3: Find coordinates of \(S\)

The coordinates of \(S\) are \((1,-4)\). Using the reflection rule \((x,y)\to(y,x)\), we get \((-4,1)\).

Step4: Find coordinates of \(Q\)

The coordinates of \(Q\) are \((-3,-10)\). Using the reflection rule \((x,y)\to(y,x)\), we get \((-10,-3)\).

Step5: Find coordinates of \(T\)

The coordinates of \(T\) are \((1,-10)\). Using the reflection rule \((x,y)\to(y,x)\), we get \((-10,1)\).

Answer:

\(R'(-4,-3)\), \(S'(-4,1)\), \(Q'(-10,-3)\), \(T'(-10,1)\)