Question

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

( r(square,square) )
( s(square,square) )
( t(square,square) )
( u(square,square) )

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 \(R\)

From the graph, \(R(-9,1)\). Using the reflection rule \((x,y)\to(y,x)\), for \(R(-9,1)\), \(x=-9\) and \(y = 1\), so \(R'(1,-9)\).

Step3: Find coordinates of \(S\)

From the graph, \(S(-9,4)\). Using the reflection rule \((x,y)\to(y,x)\), for \(S(-9,4)\), \(x=-9\) and \(y = 4\), so \(S'(4,-9)\).

Step4: Find coordinates of \(T\)

From the graph, \(T(-4,4)\). Using the reflection rule \((x,y)\to(y,x)\), for \(T(-4,4)\), \(x=-4\) and \(y = 4\), so \(T'(4,-4)\).

Step5: Find coordinates of \(U\)

From the graph, \(U(-4,1)\). Using the reflection rule \((x,y)\to(y,x)\), for \(U(-4,1)\), \(x=-4\) and \(y = 1\), so \(U'(1,-4)\).

Answer:

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