Select the coordinates A′

Question

A
′
and B′
B
′
after dilation of the line segment AB
A
B
with a scale factor of 4, centered at the origin where the endpoints are A(−2,−3)
A
(
−
2
,
−
3
)
and B (−4,−5)
B

(
−
4
,
−
5
)
.(1 point)
Responses

A′ (−2, 3)
A
′

(
−
2
,

3
)
and B′ (−4,−5)
B
′

(
−
4
,
−
5
)
upper A prime left parenthesis negative 2 comma 3 right parenthesis and upper b prime left parenthesis negative 4 comma negative 5 right parenthesis

A′ (8,12)
A
′

(
8
,
12
)
and B′(16,20)
B
′
(
16
,
20
)
upper A prime left parenthesis 8 comma 12 right parenthesis and upper B prime left parenthesis 16 comma 20 right parenthesis

A′ (−8,−12)
A
′

(
−
8
,
−
12
)
and B′ (−4,−5)
B
′

(
−
4
,
−
5
)
upper A prime left parenthesis negative 8 comma negative 12 right parenthesis and upper B prime left parenthesis negative 4 comma negative 5 right parenthesis

A′(−8,−12)
A
′
(
−
8
,
−
12
)
and B′(−16,−20)

Answer 1

To find the coordinates of points \( A' \) and \( B' \) after dilation of the line segment \( AB \) with a scale factor of 4, centered at the origin, we multiply the coordinates of each endpoint by the scale factor.

The endpoints are:

• \( A(-2, -3) \)
• \( B(-4, -5) \)

Applying the scale factor of 4:

1. For point \( A' \): \[ A' = (4 \times -2, 4 \times -3) = (-8, -12) \]

2. For point \( B' \): \[ B' = (4 \times -4, 4 \times -5) = (-16, -20) \]

So, after dilation, the coordinates are:

• \( A'(-8, -12) \)
• \( B'(-16, -20) \)

Therefore, the correct response is: A′(−8,−12) and B′(−16,−20).