Question

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 B' (2,-6)

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

A' (8,-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 center of dilation at the origin, we can use the following formula for dilation:

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

where \((x, y)\) are the original coordinates, \(k\) is the scale factor, and \((x', y')\) are the coordinates after dilation.

Given:
- Point A has coordinates \((-4, 1)\)
- Point B has coordinates \((-1, 3)\)
- Scale factor \(k = 2\)

Now we apply the formula:

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

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

After dilation, the coordinates are:
- A' is \((-8, 2)\)
- B' is \((-2, 6)\)

Thus, the dilated coordinates are:
- A' (-8, 2) and B' (-2, 6)

The correct choice is:
**A' (-8, 2) and B' (-2, 6)**.