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 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)
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 negative 8 comma 2 right parenthesis and upper B prime left parenthesis 2 comma negative 6 right parenthesis

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 apply the following formula for dilation:

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

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

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

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

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

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