Question

If ΔABC is dilated by a scale factor of 1/2

Answer 1

Point C is at (2,0)

Cut each coordinate in half to get (1,0)
2*(1/2) = 1
0*(1/2) = 0

So point C will move to (1,0)

Answer: Choice B)

Answer 2

Answer:  The correct option is (B) (1, 0).

Step-by-step explanation:  Given that ΔABC is dilated by a scale factor of $\dfrac{1}{2}$ 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

$A(0,0)\rightarrow A'\left(\dfrac{0}{2},\dfrac{0}{2}\right)=A'(0,0),\\\\B(0,3)\rightarrow B'\left(\dfrac{0}{2},\dfrac{3}{2}\right)=B'(0,1.5),\\\\C(0,0)\rightarrow C'\left(\dfrac{2}{2},\dfrac{0}{2}\right)=C'(1,0).$

Thus, the co-ordinates of point C' are (1, 0).

Option (B) is correct.