Question

△ear is rotated 180° about the origin.
draw the image of this rotation.

Explanation:

Step1: Find coordinates of \(A\), \(E\), \(R\)

Assume \(A(-6,4)\), \(E(-5,-6)\), \(R(-2,2)\)

Step2: Apply \(180^{\circ}\) rotation formula

The formula for a \(180^{\circ}\) rotation about the origin is \((x,y)\to(-x,-y)\)
For \(A(-6,4)\): \((-(-6),-4)=(6,-4)\)
For \(E(-5,-6)\): \((-(-5),-(-6))=(5,6)\)
For \(R(-2,2)\): \((-(-2),-2)=(2,-2)\)

Step3: Plot new points

Plot \(A'(6,-4)\), \(E'(5,6)\), \(R'(2,-2)\) and connect them to form \(\triangle E'A'R'\)

Answer:

Plot the points \((6,-4)\), \((5,6)\), \((2,-2)\) and draw the triangle.