Triangle abc has vertices at a(4, 2), b(1, 2), and c(4, 6) in the coordinate plane. the triangle will be rotated 270∘ counterclockwise around the point (-5, -7) and then rotated over = 0. what are the vertices of triangle a'b'c'?

a. a'(14, 2), b'(14, -1), c'(18, 2)

b. a'(0, 8), b'(0, 11), c'(-4, 8)

c. a'(-4, -16), b'(-4, -13), c'(-8, -16)

d. a'(4, 16), b'(4, 13), c'(8, 16)

D.A'(4,16),B'(4,13),C'(8,16)

Step-by-step explanation:

We are given that triangle ABC has vertices at A(4,2),B(1,2) and C(4,6) in the coordinate plane.

First we change the given points

The rule of transformation of 270 degree rotation counterclockwise about origin is given by

After rotation 270 degrees about origin

Then,

Apply the rule

Hence, the coordinates of triangle ABC after 270 degrees counterclockwise rotation around (-5,-7) is given by

After rotation y=0

The rule of transformation about y=0  is given by

Apply this rule then we get

Hence, option D is true.

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step-by-step explanation: