Question

triangle xyz has coordinates x(5, 3), y(3, 2), and z(3, 4). the triangle will be rotated 270° counterclockwise. what will be the coordinates of triangle xyz?
a x(5, 3),y(3, 2),z(3, 4)
b x(2, 5),y(2, 3),z(4, 3)
c x(3, - 5),y(2, - 3),z(4, - 3)
d x(5, - 3),y(3, - 2),z(3, - 4)

Explanation:

Step1: Recall rotation rule

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

Step2: Apply rule to point X

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

Step3: Apply rule to point Y

For $Y(3,2)$, substituting $x = 3$ and $y = 2$ into the rule $(x,y)\to(y, - x)$, we get $Y'(2,-3)$.

Step4: Apply rule to point Z

For $Z(3,4)$, substituting $x = 3$ and $y = 4$ into the rule $(x,y)\to(y, - x)$, we get $Z'(4,-3)$.

Answer:

C. $X'(3,-5),Y'(2,-3),Z'(4,-3)$