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′ (−5, −2) and B′ (−2, 6)
A′ (−8, 2) and B′ (2, −6)
A′ (8, −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 centered at the origin, we use the dilation formula:

\[
(x', y') = (k \cdot x, k \cdot y)
\]

where \(k\) is the scale factor and \((x, y)\) are the original coordinates of the points.

Given:
- Point A at \((-4, 1)\)
- Point B at \((-1, 3)\)

Now, applying the dilation with a scale factor of 2:

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

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

Thus, the coordinates after dilation are:
- \(A' = (-8, 2)\)
- \(B' = (-2, 6)\)

So, the correct answer is:
**A′ (−8, 2) and B′ (−2, 6)**