Question

graph the image of rhombus tuvw after a reflection over the line y = x.

Explanation:

Step1: Find the coordinates of the original points

From the graph, we can get the coordinates of the vertices of rhombus \(TUVW\) as \(T(-10,5)\), \(U(-4,5)\), \(V(-2,9)\), \(W(-6,9)\).

Step2: Apply the reflection rule over the line \(y = x\)

The rule for reflecting a point \((x,y)\) over the line \(y=x\) is \((x,y)\to(y,x)\).
For point \(T(-10,5)\), after reflection, it becomes \(T'(5,-10)\).
For point \(U(-4,5)\), after reflection, it becomes \(U'(5,-4)\).
For point \(V(-2,9)\), after reflection, it becomes \(V'(9,-2)\).
For point \(W(-6,9)\), after reflection, it becomes \(W'(9,-6)\).

Step3: Plot the new points and connect them

Plot the points \(T'(5,-10)\), \(U'(5,-4)\), \(V'(9,-2)\), \(W'(9,-6)\) on the coordinate plane and connect them in order to form the reflected rhombus.

Answer:

Plot the points \(T'(5,-10)\), \(U'(5,-4)\), \(V'(9,-2)\), \(W'(9,-6)\) and connect them to get the image of rhombus \(TUVW\) after reflection over the line \(y = x\).