Answer:
"A 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left" should be the right answer.
Step-by-step explanation:
Solution:
Vertices of Preimage that is Triangle ABC =A(4,-2), B(3,-2),C(3,-5)
Vertices of image , i.e Δ A'B'C'=A'(1,2),B'(2,2), C'(2,5)
Now, transalation by 5 units left of triangle ABC takes it to
A(4,-2)=(4-5,-2)=(-1,-2)
B(3,-2)=(3-5,-2)=(-2,-2)
C(3,-5)=(3-5,-5)=(-2,-5)
When preimage is rotated through an angle of 180 degree, counterclockwise vertices of triangle (-1,-2),(-2,-2) and (-2,-5) goes to image A'(1,2),B'(2,2), C'(2,5).
Option C: A translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin takes ΔABC to ΔA'B'C'.
