Question

an entire pre - image that is located in quadrant iii is then rotated 90° clockwise about the origin. in which quadrant will the image fall? quadrant i quadrant ii quadrant iii quadrant iv

Explanation:

Step1: Recall rotation rules

A 90 - degree clockwise rotation about the origin has the transformation rule \((x,y)\to(y, - x)\).

Step2: Analyze quadrant III coordinates

In quadrant III, \(x<0\) and \(y < 0\). After a 90 - degree clockwise rotation \((x,y)\to(y,-x)\), the new \(x\) - coordinate \(y<0\) and the new \(y\) - coordinate \(-x>0\).

Step3: Determine the quadrant

Points with \(x < 0\) and \(y>0\) are in quadrant II.

Answer:

Quadrant II