Answer: The correct option is (B) (1, 0).
Step-by-step explanation: Given that ΔABC is dilated by a scale factor of
with the center of dilation at the point A.
Let, the dilated triangle be ΔA'B'C'.
We are to find the co-ordinates of the point C'.
From the figure, we note that
the co-ordinates of the vertices of ΔABC are A(0, 0), B(0, 3) and C(2, 0).
Since the center of dilation is at the origin, so the co-ordinates of each vertex after dilation will be
![A(0,0)\rightarrow A'\left(\dfrac{0}{2},\dfrac{0}{2}\right)=A'(0,0),\\\\B(0,3)\rightarrow B'\left(\dfrac{0}{2},\dfrac{3}{2}\right)=B'(0,1.5),\\\\C(0,0)\rightarrow C'\left(\dfrac{2}{2},\dfrac{0}{2}\right)=C'(1,0).](https://tex.z-dn.net/?f=A%280%2C0%29%5Crightarrow%20A%27%5Cleft%28%5Cdfrac%7B0%7D%7B2%7D%2C%5Cdfrac%7B0%7D%7B2%7D%5Cright%29%3DA%27%280%2C0%29%2C%5C%5C%5C%5CB%280%2C3%29%5Crightarrow%20B%27%5Cleft%28%5Cdfrac%7B0%7D%7B2%7D%2C%5Cdfrac%7B3%7D%7B2%7D%5Cright%29%3DB%27%280%2C1.5%29%2C%5C%5C%5C%5CC%280%2C0%29%5Crightarrow%20C%27%5Cleft%28%5Cdfrac%7B2%7D%7B2%7D%2C%5Cdfrac%7B0%7D%7B2%7D%5Cright%29%3DC%27%281%2C0%29.)
Thus, the co-ordinates of point C' are (1, 0).
Option (B) is correct.