Question

pentagon nopqr is rotated 270° counterclockwise about the origin to produce pentagon nopqr. write the rule for the rotation. (x, y) → (□, □)

Explanation:

Step1: Recall rotation rules

For a \(270^\circ\) counterclockwise rotation about the origin, the transformation rule is derived from coordinate geometry. A \(270^\circ\) counterclockwise rotation is equivalent to a \(90^\circ\) clockwise rotation. The rule for a point \((x,y)\) rotated \(270^\circ\) counterclockwise about the origin is \((x,y)\to(y, -x)\). We can verify this with a simple point, say \((1,0)\). Rotating \(270^\circ\) counterclockwise, it should go to \((0, -1)\), and using the rule \((1,0)\to(0, - 1)\), which matches. Another example: \((0,1)\) rotated \(270^\circ\) counterclockwise becomes \((1,0)\), and the rule gives \((0,1)\to(1,0)\), which is correct.

Answer:

\((x, y)\to(y, -x)\)