Question

1. a square centered at the origin is rotated 270° clockwise. where does the top vertex move? a) to the left side b) to the right side c) to the bottom side d) it stays at the top 7. a figure originally in quadrant i is rotated 90° clockwise about the origin. where does the figure move? a) quadrant i b) quadrant ii c) quadrant iii d) quadrant iv

Explanation:

Step1: Understand rotation rules

A 270 - degree clockwise rotation is equivalent to a 90 - degree counter - clockwise rotation. For a point \((x,y)\) rotated 90 degrees counter - clockwise about the origin, the transformation is \((x,y)\to(-y,x)\). For a square centered at the origin, the top vertex has positive \(y\) and \(x = 0\). After a 90 - degree counter - clockwise rotation, it moves to the left side.

Step2: Analyze 90 - degree clockwise rotation

For a 90 - degree clockwise rotation of a point \((x,y)\) about the origin, the transformation is \((x,y)\to(y, - x)\). A figure in Quadrant I has positive \(x\) and positive \(y\) coordinates. After a 90 - degree clockwise rotation, the \(x\) and \(y\) values change such that it moves to Quadrant IV.

Answer:

1. A. To the left side
2. D. Quadrant IV