Question

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

Explanation:

Step1: Find the coordinates of original polygon

From the graph, the coordinates of polygon \(ABCD\) are \(A(2,-1)\), \(B(-1,1)\), \(C(1,3)\), \(D(4,1)\).

Step2: Apply the 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 \(D(4,1)\), after reflection, \(D'(1,4)\).

Step3: Plot the new points

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

Answer:

Plot the points \(A'(-1,2)\), \(B'(1,-1)\), \(C'(3,1)\), \(D'(1,4)\) and connect them.