Question

rotations as functions quick check
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)
-90 degrees (clockwise)
90 degrees (counterclockwise)
270 degrees (counterclockwise)
-180 degrees (clockwise) or 180 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 270 - degree counter - clockwise rotation, $(x,y)\to(y, - x)$.
• For a 180 - degree rotation (clockwise or counter - clockwise), $(x,y)\to(-x,-y)$.

Let the original point be $P(x,y)=(-4,10)$ and the rotated point be $P'(x',y')=(-10,-4)$.

Step2: Check 90 - degree counter - clockwise rotation

If we apply a 90 - degree counter - clockwise rotation to $P(-4,10)$, using the rule $(x,y)\to(-y,x)$, we get $(-10,-4)$.

Answer:

90 degrees (counterclockwise)