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 negative 2 comma 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)
𝐵
′

(
2
,

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

Answer 1

To find the coordinates of points A' and B' after a dilation with a scale factor of 2 and the center of dilation at the origin, we use the 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 after dilation.

For point A(-4, 1):

• Scale factor \(k = 2\)
• Original coordinates: \((-4, 1)\)

Calculating the new coordinates: \[ A' = (2 \times -4, 2 \times 1) = (-8, 2) \]

For point B(-1, 3):

• Scale factor \(k = 2\)
• Original coordinates: \((-1, 3)\)

Calculating the new coordinates: \[ B' = (2 \times -1, 2 \times 3) = (-2, 6) \]

So the coordinates of \(A'\) and \(B'\) after dilation are: \[ A'(-8, 2) \text{ and } B'(-2, 6) \]

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