Question

graph the image of kite ( abcd ) after a reflection over the line ( y = -x ).

Explanation:

Step1: Find the coordinates of the original kite

The coordinates of the vertices of kite \(ABCD\) are \(A(-7,-3)\), \(B(-5,-1)\), \(C(-7,0)\), \(D(-9,-1)\)

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 \(A(-7,-3)\):

Substitute \(x = - 7\) and \(y=-3\) into the rule \((x,y)\to(-y,-x)\)
\(A'=(3,7)\)

• For point \(B(-5,-1)\):

Substitute \(x=-5\) and \(y = - 1\) into the rule \((x,y)\to(-y,-x)\)
\(B'=(1,5)\)

• For point \(C(-7,0)\):

Substitute \(x=-7\) and \(y = 0\) into the rule \((x,y)\to(-y,-x)\)
\(C'=(0,7)\)

• For point \(D(-9,-1)\):

Substitute \(x=-9\) and \(y=-1\) into the rule \((x,y)\to(-y,-x)\)
\(D'=(1,9)\)

Answer:

Plot the points \(A'(3,7)\), \(B'(1,5)\), \(C'(0,7)\), \(D'(1,9)\) and connect them to form the reflected kite.