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

Step2: Analyze the given points

We have the original point $P(-4,10)$ and the rotated point $P'(-10,-4)$.
If we apply the 90 - degree counter - clockwise rotation rule $(x,y)\to(-y,x)$ to $P(-4,10)$:
Substitute $x=-4$ and $y = 10$ into the rule. We get $(-y,x)=(-10,-4)$ which is the coordinates of $P'$.

Answer:

B. 90 degrees (counterclockwise)