Question

if the coordinates of point p are (2,-3), then ( r_{90} circ r_{180} ) is ________.
(-2,-3)
(3,-2)
(-2,3)
(-3,-2)

Explanation:

Step1: Find the result of \(R_{180}\)

The rule for a \(180^{\circ}\) rotation \((x,y)\to(-x, -y)\).
For point \(P(2,-3)\), after \(R_{180}\), we get \((- 2,3)\).

Step2: Find the result of \(R_{90}\) on the new point

The rule for a \(90^{\circ}\) rotation \((x,y)\to(-y,x)\).
For the point \((-2,3)\) after \(R_{90}\), we substitute \(x=-2\) and \(y = 3\) into the rule: \((-3,-2)\)

Answer:

\((-3,-2)\)