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)
Responses

A′ (−8, 2)
and B′ (−2, 6)
upper a prime left parenthesis negative 8 comma 2 right parenthesis and upper b prime left parenthesis negative 2 comma 6 right parenthesis

A′ (8, −2)
and B′ (2, −6)
upper A prime left parenthesis 8 comma negative 2 right parenthesis and upper B prime left parenthesis 2 comma negative 6 right parenthesis

A′ (−5, −2)
and B′ (−2, 6)
upper A prime left parenthesis negative 5 comma negative 2 right parenthesis and upper B prime left parenthesis negative 2 comma 6 right parenthesis

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 a center of dilation at the origin, we will apply the dilation formula for each point.

The formula for dilation is given by:
\[
(x', y') = (kx, ky)
\]
where \(k\) is the scale factor, and \((x, y)\) are the original coordinates of the point.

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

Now, we can apply the dilation to each point:

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

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

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

The correct response is:
**A′ (−8, 2) and B′ (−2, 6)**.