Question

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

Explanation:

Step1: Find the coordinates of the original points

From the graph, we can see that the coordinates of the vertices of rhombus \(BCDE\) are \(B(-2,1)\), \(C(-2,6)\), \(D(1,10)\), \(E(1,5)\).

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 \(B(-2,1)\): After reflection, \(B'=(1,-2)\)
• For point \(C(-2,6)\): After reflection, \(C'=(6,-2)\)
• For point \(D(1,10)\): After reflection, \(D'=(10,1)\)
• For point \(E(1,5)\): After reflection, \(E'=(5,1)\)

Step3: Plot the new points

Plot the points \(B'(1,-2)\), \(C'(6,-2)\), \(D'(10,1)\), \(E'(5,1)\) on the coordinate - plane and connect them to form the reflected rhombus.

Answer:

The coordinates of the vertices of the reflected rhombus are \(B'(1,-2)\), \(C'(6,-2)\), \(D'(10,1)\), \(E'(5,1)\). Plot these points and connect them to get the image of rhombus \(BCDE\) after reflection over the line \(y = x\).