Question

show what you know
a triangle is rotated 90 degrees clockwise about the origin. which coordinate rule describes this transformation?
$(x,y)\to(-x,-y)$
$(x,y)\to(y,-x)$
$(x,y)\to(x,-y)$
$(x,y)\to(-y,x)$

Explanation:

Step1: Recall rotation rules

When rotating a point \((x,y)\) \(90^{\circ}\) clockwise about the origin, we use the rule \((x,y)\to(y, -x)\).
Let's take a sample point \((1,2)\).
For \((x,y)=(1,2)\):

• If we use \((x,y)\to(-x,-y)\), we get \((-1,-2)\) (this is \(180^{\circ}\) rotation).
• If we use \((x,y)\to(y,-x)\), we get \((2,-1)\).
• If we use \((x,y)\to(x,-y)\), we get \((1,-2)\) (this is reflection over \(x -\)axis).
• If we use \((x,y)\to(-y,x)\), we get \((-2,1)\) (this is \(90^{\circ}\) counter - clockwise rotation).

Answer:

\((x,y)\to(y, -x)\)