Question

1. find the coordinates of the vertices of each figure after the given transformation. rotation 270° counterclockwise about the origin. p(-4, 2), q(-5, 3), r(-1, 4)

Explanation:

Step1: Recall rotation rule

The rule for a 270 - degree counter - clockwise rotation about the origin is $(x,y)\to(y, - x)$.

Step2: Apply rule to point P

For $P(-4,2)$, substituting $x=-4$ and $y = 2$ into the rule $(x,y)\to(y, - x)$, we get $P'(2,4)$.

Step3: Apply rule to point Q

For $Q(-5,3)$, substituting $x=-5$ and $y = 3$ into the rule $(x,y)\to(y, - x)$, we get $Q'(3,5)$.

Step4: Apply rule to point R

For $R(-1,4)$, substituting $x=-1$ and $y = 4$ into the rule $(x,y)\to(y, - x)$, we get $R'(4,1)$.

Answer:

$P'(2,4), Q'(3,5), R'(4,1)$