Question

what is the image of the point (3, -8) after a rotation of 90° counterclockwise about the origin? answer

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise about the origin, the new coordinates \((x',y')\) are given by the transformation \((x,y)\to(-y,x)\).

Step2: Apply the rule to the given point

For the point \((3,-8)\), here \(x = 3\) and \(y=-8\).
Substitute \(x = 3\) and \(y = - 8\) into the formula \((x',y')=(-y,x)\).
We get \(x'=-(-8)=8\) and \(y'=3\).

Answer:

\((8,3)\)