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

• Rotation of \(90^{\circ}\) clockwise: \((x,y)\to(y, -x)\)
• Rotation of \(90^{\circ}\) counter - clockwise: \((x,y)\to(-y,x)\)
• Rotation of \(180^{\circ}\): \((x,y)\to(-x,-y)\)
• Rotation of \(270^{\circ}\) clockwise: \((x,y)\to(-y,x)\) (same as \(90^{\circ}\) counter - clockwise)
• Rotation of \(270^{\circ}\) counter - clockwise: \((x,y)\to(y, -x)\) (same as \(90^{\circ}\) clockwise)

Point \(A=(0,5)\) and \(A'=(5,0)\)

Step2: Apply rotation rules

• For \(90^{\circ}\) clockwise rotation: If \(A=(0,5)\), then \((x = 0,y = 5)\), using \((x,y)\to(y,-x)\) gives \((5,0)\)
• For \(270^{\circ}\) counter - clockwise rotation: If \(A=(0,5)\), then \((x = 0,y = 5)\), using \((x,y)\to(y,-x)\) gives \((5,0)\)

Answer:

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