Answer:
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
[tex]A_1=(4+5,2+7)=(9,9)[/tex]
[tex]B_1=(1+5,2+7)=(6,9)[/tex]
[tex]C_1=(4+5,6+7)=(9,13)[/tex]
The rule of transformation of 270 degree rotation counterclockwise about origin is given by
[tex](x,y)\rightarrow (y,-x)[/tex]
After rotation 270 degrees about origin
Then, [tex]A_2=(9,-9)[/tex]
[tex]B_2=(9,-6)[/tex]
[tex]C_2=(13,-9)[/tex]
Apply the rule
[tex](x,y)\rightarrow (x-5, y-7)[/tex]
[tex]A_3=(4,-16)[/tex]
[tex]B_3=(4,-13)[/tex]
[tex]C_3=(8,-16)[/tex]
Hence, the coordinates of triangle ABC after 270 degrees counterclockwise rotation around (-5,-7) is given by
[tex]A_3=(4,-16),B_3=(4,-13),C_3=(8,-16)[/tex]
After rotation y=0
The rule of transformation about y=0 is given by
[tex](x,y)\rightarrow (x,-y)[/tex]
Apply this rule then we get
[tex]A'=(4,16)[/tex]
[tex]B'=(4,13)[/tex]
[tex]C'=(8,16)[/tex]
Hence, option D is true.
