Question

Dilations Quick Check

Line AB contains point A (4, 1) and point B (1, 3) Find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin. (1 point)

A(-8, 2) and B (-2, 6)

A' (8,2) and F (2,6)

A (8, 2) and B (2,6)

A (5,2) and B (-2, 6)

Answer 1

To find the coordinates of points A and B after a dilation with a scale factor of 2 and a center of dilation at the origin, we can apply the dilation formula:

If \( (x, y) \) is a point and the center of dilation is the origin (0, 0), then after dilation with a scale factor \( k \), the new coordinates \( (x', y') \) are given by:

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

For point A (4, 1):
\[
A' = (2 \times 4, 2 \times 1) = (8, 2)
\]

For point B (1, 3):
\[
B' = (2 \times 1, 2 \times 3) = (2, 6)
\]

Thus, after the dilation, the coordinates of A' and B' are:

A' (8, 2) and B' (2, 6).

So, the correct answer is:

**A' (8, 2) and B' (2, 6)**.