Question

the point p (-1,2) is rotated to become p (2,1). describe the rotation by degree and direction.
(1 point)

• 270° rotation

180° rotation

• 90° rotation

90° rotation

Explanation:

Step1: Recall rotation rules

For a point $(x,y)$ rotated about the origin:

• A $90^{\circ}$ counter - clockwise rotation gives $(-y,x)$.
• A $180^{\circ}$ rotation gives $(-x,-y)$.
• A $- 90^{\circ}$ (or $270^{\circ}$ counter - clockwise) rotation gives $(y,-x)$.
• A $-270^{\circ}$ (or $90^{\circ}$ clockwise) rotation gives $(-y,x)$.

The original point is $P(-1,2)$ and the new point is $P'(2,1)$.
If we consider the rotation rules, when we rotate a point $(x,y)$ by $-90^{\circ}$ (clockwise $90^{\circ}$) about the origin, the transformation is $(x,y)\to(y, - x)$. For $P(-1,2)$, when we apply the $-90^{\circ}$ rotation rule: $x=-1,y = 2$, and the new point is $(2,1)$.

Answer:

C. $-90^{\circ}$ rotation