Question

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

with a dilation center of A, what will be the coordinates of point C'?
A) (0, 0)
B) (1, 0)
C) (0, 1)
D) (4, 0)

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
`(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((0)/(2),(0)/(2)\right)=A'(0,0),\\\\B(0,3)\rightarrow B'\left((0)/(2),(3)/(2)\right)=B'(0,1.5),\\\\C(0,0)\rightarrow C'\left((2)/(2),(0)/(2)\right)=C'(1,0).`

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

Option (B) is correct.