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

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 from the origin, we can use the dilation formula:

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

where \( (x, y) \) are the original coordinates, \( (x', y') \) are the dilated coordinates, and \( k \) is the scale factor (in this case, \( k = 2 \)).

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

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

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

- \( A' (-8, 2) \)
- \( B' (-2, 6) \)

The correct response is:

**A′ (−8, 2) and B′ (−2, 6)**.