Question

rotations
draw the following triangle after a 180° rotation about the origin.

Explanation:

Step1: Apply rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) about the origin, the new coordinates are \((-x,-y)\).
For the point \((3,1)\):
\(x = 3,y = 1\), new \(x=-3\), new \(y = - 1\), so the new point is \((-3,-1)\)

Step2: Apply rotation rule

For the point \((-3,-3)\):
\(x=-3,y = - 3\), new \(x = 3\), new \(y=3\), so the new point is \((3,3)\)

Step3: Apply rotation rule

For the point \((-4,-8)\):
\(x=-4,y=-8\), new \(x = 4\), new \(y = 8\), so the new point is \((4,8)\)

Answer:

The new vertices of the triangle after \(180^{\circ}\) rotation about the origin are \((-3,-1)\), \((3,3)\) and \((4,8)\)