Question

reflect the figure over the line x = -1. write new coordinates.

4). reflect the figure over y = -2. write new coordinates.

Explanation:

Step1: Find original coordinates

For parallelogram \(ABCD\):

• \(A(2,1)\)
• \(B(-2,5)\)
• \(C(-5,-2)\)
• \(D(-1,-6)\)

For triangle \(ABC\):

• \(A(6,6)\)
• \(B(0,-2)\)
• \(C(-4,2)\)

Step2: Reflect over \(x = - 1\)

The formula for reflecting a point \((x,y)\) over the line \(x=a\) is \((2a - x,y)\). Here \(a=-1\), so the new \(x\) - coordinate is \(2\times(-1)-x=-2 - x\), and \(y\) remains the same.

• \(A'(2\times(-1)-2,1)=(-4,1)\)
• \(B'(2\times(-1)-(-2),5)=(0,5)\)
• \(C'(2\times(-1)-(-5),-2)=(3,-2)\)
• \(D'(2\times(-1)-(-1),-6)=(-1,-6)\)

Step3: Reflect over \(y=-2\)

The formula for reflecting a point \((x,y)\) over the line \(y = b\) is \((x,2b - y)\). Here \(b = - 2\), so the new \(y\) - coordinate is \(2\times(-2)-y=-4 - y\), and \(x\) remains the same.

• \(A'(6,2\times(-2)-6)=(6,-10)\)
• \(B'(0,2\times(-2)-(-2))=(0,-2)\)
• \(C'(-4,2\times(-2)-2)=(-4,-6)\)

Answer:

Parallelogram \(ABCD\)	Parallelogram \(A'B'C'D'\)
\(B(-2,5)\)	\(B'(0,5)\)
\(C(-5,-2)\)	\(C'(3,-2)\)
\(D(-1,-6)\)	\(D'(-1,-6)\)

Triangle \(ABC\)	Triangle \(A'B'C'\)
\(B(0,-2)\)	\(B'(0,-2)\)
\(C(-4,2)\)	\(C'(-4,-6)\)