Question

map the coordinates of the reflection of trapezoid qrst with vertices q(4, -1), r(6, -1), s(8, -6) and t(2, -6): in the line y = x

Explanation:

Step1: Recall reflection over \( y = x \)

The rule for reflecting a point \((x, y)\) over the line \( y = x \) is to swap the \( x \)-coordinate and the \( y \)-coordinate, so the image of \((x, y)\) is \((y, x)\).

Step2: Reflect point \( Q(4, -1) \)

Using the rule, for \( Q(4, -1) \), swap \( x \) and \( y \). So the reflected point \( Q' \) is \((-1, 4)\).

Step3: Reflect point \( R(6, -1) \)

For \( R(6, -1) \), applying the reflection rule, swap \( x \) and \( y \). The reflected point \( R' \) is \((-1, 6)\).

Step4: Reflect point \( S(8, -6) \)

For \( S(8, -6) \), using the reflection rule, swap \( x \) and \( y \). The reflected point \( S' \) is \((-6, 8)\).

Step5: Reflect point \( T(2, -6) \)

For \( T(2, -6) \), applying the reflection rule, swap \( x \) and \( y \). The reflected point \( T' \) is \((-6, 2)\).

Answer:

The coordinates of the reflection of trapezoid \( QRST \) over the line \( y = x \) are \( Q'(-1, 4) \), \( R'(-1, 6) \), \( S'(-6, 8) \), and \( T'(-6, 2) \).