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 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)
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 use the formula for dilation:

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

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

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

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

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

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