Question

triangle xyz has vertices x(1, 3), y(0, 0), and z(-1, 2). the image of triangle xyz after a rotation has vertices x(-3, 1), y(0, 0), and z(-2, -1). which rule describes the transformation? r_{0,90^{circ}} r_{0,180^{circ}} r_{0,270^{circ}} r_{0,360^{circ}}

Explanation:

Step1: Recall rotation rules

• 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 \(270^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(y, - x)\)
• The rule for a \(360^{\circ}\) rotation about the origin \((x,y)\to(x,y)\)

Step2: Apply the rules to a point

Take point \(X(1,3)\)

• For a \(90^{\circ}\) counter - clockwise rotation: \((1,3)\to(-3,1)\)
• For a \(180^{\circ}\) rotation: \((1,3)\to(-1,-3)\)
• For a \(270^{\circ}\) counter - clockwise rotation: \((1,3)\to(3,-1)\)
• For a \(360^{\circ}\) rotation: \((1,3)\to(1,3)\)

Answer:

\(R_{0,90^{\circ}}\)