Question

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

Explanation:

Step1: Find the coordinates of the original polygon

From the graph, we can see that the coordinates of the vertices of the polygon are \(A(6, - 3)\), \(B(1, - 2)\), \(C(4,1)\).

Step2: Apply the reflection rule

The rule for reflecting a point \((x,y)\) over the line \(y = x\) is \((x,y)\to(y,x)\).
For point \(A(6,-3)\), after reflection, the new point \(A'(-3,6)\).
For point \(B(1,-2)\), after reflection, the new point \(B'(-2,1)\).
For point \(C(4,1)\), after reflection, the new point \(C'(1,4)\).

Step3: Plot the new points

Plot the points \(A'(-3,6)\), \(B'(-2,1)\), \(C'(1,4)\) on the coordinate plane and connect them to form the reflected polygon.

Answer:

The coordinates of the reflected polygon are \(A'(-3,6)\), \(B'(-2,1)\), \(C'(1,4)\). Plot these points and connect them.