Question

triangle def has coordinates d(4, -1), e(5, 2), and f(1, 2). determine the coordinates of the vertices of the image after a rotation 270° counterclockwise about the origin.

a) d(-4, 1), e(-5, -2), and f(-1, -2)
b) d(1, 0), e(2, 3), and f(-2, 3)
c) d(-1, -4), e(2, -5), and f(2, -1)
d) d(5, -1), e(6, 2), and f(2, 2)

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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 D

For point $D(4,-1)$, using the rule $(x,y)\to(y, - x)$, we get $D'( - 1,-4)$.

Step3: Apply rule to point E

For point $E(5,2)$, using the rule $(x,y)\to(y, - x)$, we get $E'(2,-5)$.

Step4: Apply rule to point F

For point $F(1,2)$, using the rule $(x,y)\to(y, - x)$, we get $F'(2,-1)$.

Answer:

C. $D'(-1,-4), E'(2,-5),$ and $F'(2,-1)$