Line AB

Question

𝐴
𝐵
contains point A(1, 2)
𝐴
(
1
,

2
)
and point B (−2, −1)
𝐵

(
−
2
,

−
1
)
. Find the coordinates of A′
𝐴
′
and B′
𝐵
′
after a dilation with a scale factor of 5 with a center point of dilation at the origin.(1 point)
Responses

A′ (5, 10)
𝐴
′

(
5
,

10
)

and B′ (10, 5)
𝐵
′

(
10
,


5
)
upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis 10 comma 5 right parenthesis

A′ (5, 10)
𝐴
′

(
5
,

10
)

and B′ (−2, −1)
𝐵
′

(
−
2
,

−
1
)
upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis negative 2 comma negative 1 right parenthesis

A′ (5, 10)
𝐴
′

(
5
,

10
)

and B′ (−10, −5)
𝐵
′

(
−
10
,

−
5
)
upper A prime left parenthesis 5 comma 10 right parenthesis and upper B prime left parenthesis negative 10 comma negative 5 right parenthesis

A′

Answer 1

To find the coordinates of points A' and B' after a dilation with a scale factor of 5 and center point at the origin (0, 0), we use the following formula for dilation:

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

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

Given:

• Point A (1, 2)
• Point B (-2, -1)
• Scale factor \( k = 5 \)

Now applying the formula:

1. For point A (1, 2): \[ A' = (5 \cdot 1, 5 \cdot 2) = (5, 10) \]

2. For point B (-2, -1): \[ B' = (5 \cdot -2, 5 \cdot -1) = (-10, -5) \]

Thus, the coordinates after dilation will be:

• \( A' (5, 10) \)
• \( B' (-10, -5) \)

The correct response is: A′ (5, 10) and B′ (−10, −5).