Question

a point is rotated about the origin. its coordinates are (p(-4,10)) and (p(-10,-4)). determine the degree of rotation and direction by applying rotation mapping. (1 point)

270 degrees (counterclockwise)

-90 degrees (clockwise)

-180 degrees (clockwise) or 180 degrees (counterclockwise)

90 degrees (counterclockwise)

Explanation:

Step1: Recall rotation rules

The rotation rules about the origin are:

• For a 90 - degree counter - clockwise rotation: $(x,y)\to(-y,x)$
• For a 180 - degree rotation (clockwise or counter - clockwise): $(x,y)\to(-x,-y)$
• For a 270 - degree counter - clockwise (or 90 - degree clockwise) rotation: $(x,y)\to(y, - x)$

Given $P(-4,10)$ and $P'(-10,-4)$.
If we consider the 90 - degree counter - clockwise rotation rule, when we rotate the point $P(x = - 4,y = 10)$ 90 degrees counter - clockwise, we substitute $x=-4$ and $y = 10$ into the rule $(x,y)\to(-y,x)$. So $(-4,10)\to(-10,-4)$.

Answer:

D. 90 degrees (counterclockwise)