Question

graph the image of the polygon after a reflection in the line y = x

Explanation:

Step1: Find coordinates of original polygon

Assume the coordinates of the polygon vertices \(A(2, - 1)\), \(B(-1,1)\), \(C(1,3)\), \(D(4,2)\)

Step2: Apply reflection rule

The rule for reflection over the line \(y = x\) is \((x,y)\to(y,x)\)

• For point \(A(2,-1)\), after reflection \(A'(-1,2)\)
• For point \(B(-1,1)\), after reflection \(B'(1,-1)\)
• For point \(C(1,3)\), after reflection \(C'(3,1)\)
• For point \(D(4,2)\), after reflection \(D'(2,4)\)

Step3: Plot the new points

Plot the points \(A'(-1,2)\), \(B'(1,-1)\), \(C'(3,1)\), \(D'(2,4)\) on the coordinate plane and connect them to form the reflected polygon.

Answer:

Plot the points \((-1,2)\), \((1,-1)\), \((3,1)\), \((2,4)\) and connect them.