Answer:
The correct option is C.
Step-by-step explanation:
From the given graph it is clear that the vertices of triangle ABC are A(4,-2), B(3,-2) and C(3,-5).
The vertices of triangle A'B'C' are A'(1,2), B'(2,2) and C'(2,5).
If a figure translated 5 units left, then
[tex](x,y)\rightarrow (x-5,y)[/tex]
The vertices of triangle after translation are
[tex]A(4,-2)\rightarrow A_1(-1,-2)[/tex]
[tex]B(3,-2)\rightarrow B_1(-2,-2)[/tex]
[tex]C(3,-5)\rightarrow C_1(-2,-5)[/tex]
If a figure rotated 180° counterclockwise about the origin then
[tex](x,y)\rightarrow (-x,-y)[/tex]
The vertices of triangle after rotation are
[tex]A_1(-1,-2)\rightarrow A'(1,2)[/tex]
[tex]B_1(-2,-2)\rightarrow B'(2,2)[/tex]
[tex]C_1(-2,-5)\rightarrow C'(2,5)[/tex]
The set transformation is " A translation 5 units to the left followed by a 180° counterclockwise about the origin".
Therefore the correct option is C.
