Question

the point p ( - 1, 2 ) is rotated to become p ( 2, 1 ). describe the rotation by degree and direction. note: make a difference between positive and negative values as it relates to clockwise and counterclockwise directions (1 point) -270 degrees rotation -90 degrees rotation 90 degrees rotation 180 degrees rotation

Explanation:

Step1: Recall rotation rules

In a 2 - D coordinate system, 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 $270^{\circ}$ counter - clockwise (or $- 90^{\circ}$ clockwise) rotation gives $(y,-x)$.

Step2: Analyze given points

The original point is $P(-1,2)$ and the rotated point is $P'(2,1)$. If we consider the rotation rules, when we rotate a point $(x,y)$ by $90^{\circ}$ counter - clockwise about the origin, the transformation is $(x,y)\to(-y,x)$. For $P(-1,2)$, if we rotate it $90^{\circ}$ counter - clockwise, we get $(-2,-1)$ which is not correct. If we rotate it $180^{\circ}$, we get $(1, - 2)$ which is not correct. If we rotate it $270^{\circ}$ counter - clockwise (or $-90^{\circ}$ clockwise), for a point $(x,y)$ the transformation is $(y,-x)$. For $P(-1,2)$, when we apply the $-90^{\circ}$ (clockwise) rotation rule $(y,-x)$, we substitute $x=-1$ and $y = 2$ and get $(2,1)$ which is the point $P'$.

Answer:

-90 degrees rotation