Question

1. what happens to the pre - image coordinates when you rotate 90° clockwise?
2. what happens to the pre - image coordinates when you rotate 90° counterclockwise?
3. what happens to the pre - image coordinates when you rotate 180°?

Explanation:

Step1: Determine the rotation rules

For a \(90^{\circ}\) clockwise rotation, the rule is \((x,y)\to(y, -x)\).
For a \(90^{\circ}\) counter - clockwise rotation, the rule is \((x,y)\to(-y,x)\).
For a \(180^{\circ}\) rotation, the rule is \((x,y)\to(-x,-y)\).

Step2: Analyze the pre - image and image coordinates

Let's assume a general point \((x,y)\) in the pre - image.

• For \(90^{\circ}\) clockwise rotation:

If we have a point \(A(x,y)\) in the pre - image, after a \(90^{\circ}\) clockwise rotation, its image \(A'(y,-x)\).

• For \(90^{\circ}\) counter - clockwise rotation:

If we have a point \(A(x,y)\) in the pre - image, after a \(90^{\circ}\) counter - clockwise rotation, its image \(A''(-y,x)\).

• For \(180^{\circ}\) rotation:

If we have a point \(A(x,y)\) in the pre - image, after a \(180^{\circ}\) rotation, its image \(A'''(-x,-y)\).

Answer:

1. When you rotate \(90^{\circ}\) clockwise, the pre - image coordinates \((x,y)\) change to \((y, -x)\).
2. When you rotate \(90^{\circ}\) counter - clockwise, the pre - image coordinates \((x,y)\) change to \((-y,x)\).
3. When you rotate \(180^{\circ}\), the pre - image coordinates \((x,y)\) change to \((-x,-y)\).