Line AB

Question

A
B
contains point A(−4, 1)
A
(
−
4
,

1
)
and point B (−1, 3)
B

(
−
1
,

3
)
. Find the coordinates of A′
A
′
and B′
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)
A
′

(
−
8
,

2
)

and B′ (2, −6)
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′ (8, −2)
A
′

(
8
,

−
2
)

and B′ (2, −6)
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)
A
′

(
−
5
,

−
2
)

and B′ (−2, 6)
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)
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 from the origin, we can use the following formula for dilation:

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

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

For point A \((-4, 1)\):

\[ A' = (2 \times -4, 2 \times 1) = (-8, 2) \]

For point B \((-1, 3)\):

\[ B' = (2 \times -1, 2 \times 3) = (-2, 6) \]

Thus, the coordinates after dilation are:

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

The correct response is:

A′ (−8, 2) and B′ (−2, 6)