Question

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)

Answer 1

ITS D

Explanation:

Answer 2

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

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

`A_1=(4+5,2+7)=(9,9)`

`B_1=(1+5,2+7)=(6,9)`

`C_1=(4+5,6+7)=(9,13)`

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

`(x,y)\rightarrow (y,-x)`

After rotation 270 degrees about origin

Then,
`A_2=(9,-9)`

`B_2=(9,-6)`

`C_2=(13,-9)`

Apply the rule

`(x,y)\rightarrow (x-5, y-7)`

`A_3=(4,-16)`

`B_3=(4,-13)`

`C_3=(8,-16)`

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

`A_3=(4,-16),B_3=(4,-13),C_3=(8,-16)`

After rotation y=0

The rule of transformation about y=0 is given by

`(x,y)\rightarrow (x,-y)`

Apply this rule then we get

`A'=(4,16)`

`B'=(4,13)`

`C'=(8,16)`

Hence, option D is true.