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′ (1, 2)
A
′

(
1
,

2
)

and B′ (−10, −5)
B
′

(
−
10
,

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

(
5
,

10
)

and B′ (−2, −1)

Answer 1

To find the coordinates of points A′ and B′ after a dilation from the origin with a scale factor of 5, we can use the formula for dilation:

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

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

Given:

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

Calculating the coordinates for A′: \[ A' = (5 \cdot 1, 5 \cdot 2) = (5, 10) \]

Calculating the coordinates for B′: \[ B' = (5 \cdot -2, 5 \cdot -1) = (-10, -5) \]

Therefore, after the dilation, the coordinates are:

• A′(5, 10)
• B′(-10, -5)

The correct response is:

A′ (5, 10) and B′ (−10, −5).