Answer:
The correct option is C.
Step-by-step explanation:
From the given figure it is clear that the vertices of figure ABC are A(-2,2), B(0,5) and C(2,2).
The vertices of figure A''B''C'' are A''(0,-2), B''(-2,-5) and C''(-4,-2).
If a figure translated two units right then
![(x,y)\rightarrow (x+2,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%20%28x%2B2%2Cy%29)
![A(-2,2)\rightarrow A'(0,2)](https://tex.z-dn.net/?f=A%28-2%2C2%29%5Crightarrow%20A%27%280%2C2%29)
![B(0,5)\rightarrow B'(2,5)](https://tex.z-dn.net/?f=B%280%2C5%29%5Crightarrow%20B%27%282%2C5%29)
![C(2,2)\rightarrow C'(4,2)](https://tex.z-dn.net/?f=C%282%2C2%29%5Crightarrow%20C%27%284%2C2%29)
After that the figure rotated 180° clockwise about the origin.
![(x,y)\rightarrow (-x,-y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Crightarrow%20%28-x%2C-y%29)
![A'(0,2)\rightarrow A''(0,-2)](https://tex.z-dn.net/?f=A%27%280%2C2%29%5Crightarrow%20A%27%27%280%2C-2%29)
![B'(2,5)\rightarrow B''(-2,-5)](https://tex.z-dn.net/?f=B%27%282%2C5%29%5Crightarrow%20B%27%27%28-2%2C-5%29)
![C'(4,2)\rightarrow C''(-4,-2)](https://tex.z-dn.net/?f=C%27%284%2C2%29%5Crightarrow%20C%27%27%28-4%2C-2%29)
Therefore ΔABC translated 2 units right, then rotated 180° clockwise about the origin.
Hence the correct option is C.