Question

triangle abc was rotated about the origin which rule describes the rotation?
$r_{0,}90^{circ}$
$r_{0,}180^{circ}$
$r_{0,}270^{circ}$
$r_{0,}360^{circ}$

Explanation:

Step1: Recall rotation rules

• \(R_{0,90^{\circ}}\): \((x,y)\to(-y,x)\)
• \(R_{0,180^{\circ}}\): \((x,y)\to(-x,-y)\)
• \(R_{0,270^{\circ}}\): \((x,y)\to(y,-x)\)
• \(R_{0,360^{\circ}}\): \((x,y)\to(x,y)\)

Step2: Check coordinates

Assume \(A=(1,4)\), \(B=(3,4)\), \(C=(2,2)\)
After rotation, \(A'=(-4,1)\), \(B'=(-4,3)\), \(C'=(-2,2)\)
Using \(R_{0,270^{\circ}}\):
For \(A(1,4)\), \((x = 1,y = 4)\to(y,-x)=(4,-1)\) (Wrong)
For \(R_{0,90^{\circ}}\): \((1,4)\to(-4,1)\)
For \(B(3,4)\): \((3,4)\to(-4,3)\)
For \(C(2,2)\): \((2,2)\to(-2,2)\)

Answer:

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