Question

point ( a ) is the image of point ( a ) under a rotation about the origin, ( (0,0) ).

determine the angles of rotation.

choose all answers that apply:

a ( 90^{circ} ) clockwise

b ( 90^{circ} ) counterclockwise

c ( 180^{circ} )

d ( 270^{circ} ) clockwise

e ( 270^{circ} ) counterclockwise

Explanation:

Step1: Recall rotation rules

The rule for a \(90^{\circ}\) clockwise rotation about the origin \((x,y)\to(y, - x)\). The rule for a \(90^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(-y,x)\). The rule for a \(180^{\circ}\) rotation about the origin \((x,y)\to(-x,-y)\). The rule for a \(270^{\circ}\) clockwise rotation about the origin \((x,y)\to(y, - x)\) (same as \(90^{\circ}\) counter - clockwise). The rule for a \(270^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(-y,x)\) (same as \(90^{\circ}\) clockwise).
Point \(A=(0,5)\) (assuming \(x = 0,y = 5\)).

Step2: Apply rotation rules

For \(90^{\circ}\) clockwise rotation: \((0,5)\to(5,0)\).
For \(90^{\circ}\) counter - clockwise rotation: \((0,5)\to(- 5,0)\).
For \(180^{\circ}\) rotation: \((0,5)\to(0,-5)\).
For \(270^{\circ}\) clockwise rotation (equivalent to \(90^{\circ}\) counter - clockwise): \((0,5)\to(-5,0)\).
For \(270^{\circ}\) counter - clockwise rotation (equivalent to \(90^{\circ}\) clockwise): \((0,5)\to(5,0)\).

Answer:

A. \(90^{\circ}\) clockwise, E. \(270^{\circ}\) counterclockwise