Question

Find the dilation of 0.25 with center (0, 0) for the following points if A (0, -4) B (5, 2)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the dilation of a point with respect to a center and scale factor, you can use the formula:

Dilated point = (scale factor) * (point - center) + center

Given that the scale factor is 0.25 and the center is (0, 0), we can find the dilated points of A and B as follows:

For point A (0, -4):
Dilated A = 0.25 * ((0, -4) - (0, 0)) + (0, 0)
Dilated A = 0.25 * (0, -4) + (0, 0)
Dilated A = (0, -1) + (0, 0)
Dilated A = (0, -1)

So, the dilation of point A (0, -4) with a center of (0, 0) and scale factor of 0.25 is (-.1).

For point B (5, 2):
Dilated B = 0.25 * ((5, 2) - (0, 0)) + (0, 0)
Dilated B = 0.25 * (5, 2) + (0, 0)
Dilated B = (1.25, 0.5) + (0, 0)
Dilated B = (1.25, 0.5)

So, the dilation of point B (5, 2) with a center of (0, 0) and scale factor of 0.25 is (1.25, 0.5)