Question

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

Explanation:

Step1: Find the coordinates of original polygon

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

Step2: Apply the reflection rule

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

For point \(A(-3,1)\):
Substitute \(x=-3\) and \(y = 1\) into the rule \((x,y)\to(-y,-x)\)
\(A'(-1,3)\)

For point \(B(1,-1)\):
Substitute \(x = 1\) and \(y=-1\) into the rule \((x,y)\to(-y,-x)\)
\(B'(1,-1)\)

For point \(C(-1,-3)\):
Substitute \(x=-1\) and \(y =-3\) into the rule \((x,y)\to(-y,-x)\)
\(C'(3,1)\)

For point \(D(-4,-2)\):
Substitute \(x=-4\) and \(y=-2\) into the rule \((x,y)\to(-y,-x)\)
\(D'(2,4)\)

Step3: Plot the new points

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

Answer:

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