Find the dilation of 0.25 with the center (0, 0) for the following points:

Question

A (0,−4)

B (0, 2)
(2 points)

Answer 1

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

\[ D(x, y) = (kx, ky) \]

where \( D(x, y) \) is the dilated point, \( (x, y) \) is the original point, \( k \) is the scale factor, and the center of dilation is at the origin (0, 0).

Here, we have a dilation factor \( k = 0.25 \).

For Point A (0, -4):

1. Apply the dilation formula: \[ D(0, -4) = (0.25 \cdot 0, 0.25 \cdot -4) = (0, -1) \]

So the dilated point A is: \[ A' = (0, -1) \]

For Point B (0, 2):

1. Apply the dilation formula: \[ D(0, 2) = (0.25 \cdot 0, 0.25 \cdot 2) = (0, 0.5) \]

So the dilated point B is: \[ B' = (0, 0.5) \]

Final Results:

• The dilation of point A (0, -4) is \( A' = (0, -1) \).
• The dilation of point B (0, 2) is \( B' = (0, 0.5) \).