Question

what is the image of the point (6,9) after a rotation of 270° counterclockwise about the origin?

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(270^{\circ}\) counter - clockwise about the origin, the transformation rule is \((x,y)\to(y, - x)\).

Step2: Apply the rule to the given point

For the point \((6,9)\), here \(x = 6\) and \(y=9\).
Substitute \(x = 6\) and \(y = 9\) into the rule \((x,y)\to(y,-x)\).
We get \((9,-6)\).

Answer:

\((9,-6)\)