A triangle has vertices at A(–2, 4), B(–2, 8), and C(6, 4). If A prime has coordinates of (–0.25, 0.5) after the triangle has been dilated with a center of dilation about the origin, which statements are true? Check all that apply. - The coordinates of C prime are (0.75, 0.5).
- The coordinates of C prime are (1.5, 1).
- The scale factor is One-eighth.
- The scale factor is 8.
- The scale factor is One-fourth.
- The scale factor is 4.
- The coordinates of B prime are (–0.25, 1).
- The coordinates of B prime are (–0.5, 2).

i think it is C

Step-by-step explanation:

When we are given a point P(x, y) centered at origin with a scale factor of k, then the dilated point will be given by P' (kx, ky)

Applying the concept:

Given A(-2, 4) and A'(-0.25, 0.5), which means , and .

Substituting -2 for x in the equation , we get the below equation:

Now we need to find B' and C' by multiplying 0.125 with the x-coordinate and y-coordinate.

x-coordinate of B is -2, y-coordinate of B is 8

x-coordinate of B'

y-coordinate of B'

So

x-coordinate of C is 6 and y-coordinate of C is 4

x-coordinate of C'

y-coordinate of C'

So

Conclusion:

The below are the TRUE statements:

(i) The coordinates of C' are (0.75, 0.5)

(ii) The scale factor is 1/8

(iii) The coordinates of B' are (–0.25, 1).

Step-by-step explanation:

(a) the volume of the cone is 20/3 in3

hence, option a is correct.