Question

triangle abc has coordinates a(2, 0), b(-1, 5), and c(4, 3). determine the coordinates of the vertices of the image after a rotation 90° counter - clockwise about the origin.
a) a(0, 2), b(-5, -1), and c(-3, 4)
b) a(2, 0), b(-1, -5), and c(4, -3)
c) a(2, 2), b(-1, 7), and c(4, 5)
d) a(-2, 0), b(1, -5), and c(-4, -3)

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$.

Step2: Rotate point A

For point $A(2,0)$, applying the rule: $x = 2,y = 0$, then $A'=(-0,2)=(0,2)$.

Step3: Rotate point B

For point $B(-1,5)$, applying the rule: $x=-1,y = 5$, then $B'=(-5,-1)$.

Step4: Rotate point C

For point $C(4,3)$, applying the rule: $x = 4,y = 3$, then $C'=(-3,4)$.

Answer:

A. A'(0, 2), B'(-5, -1), and C'(-3, 4)