Question

Select the coordinates A′
𝐴
′
and B′
𝐵
′
after dilation of the line segment AB
𝐴
𝐵
with a scale factor of 2, centered at the origin where the endpoints are A(3,7)
𝐴
(
3
,
7
)
and B(4,9)
𝐵
(
4
,
9
)
.(1 point)
Responses

A′(6,14)
𝐴
′
(
6
,
14
)
and B′(8,18)
𝐵
′
(
8
,
18
)
upper A prime left parenthesis 6 comma 14 right parenthesis and upper B prime left parenthesis 8 comma 18 right parenthesis

A′(−6,3)
𝐴
′
(
−
6
,
3
)
and B′(8,18)
𝐵
′
(
8
,
18
)
upper A prime left parenthesis negative 6 comma 3 right parenthesis and upper B prime left parenthesis 8 comma 18 right parenthesis

A′(6,14)
𝐴
′
(
6
,
14
)
and B′(−4,3)
𝐵
′
(
−
4
,
3
)
upper A prime left parenthesis 6 comma 14 right parenthesis and upper B prime left parenthesis negative 4 comma 3 right parenthesis

A′(32,72)
𝐴
′
(
3
2
,
7
2
)
and B′(2,92)

Answer 1

To find the coordinates of points \( A' \) and \( B' \) after dilation with a scale factor of 2 centered at the origin, we can use the formula for dilation:

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

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

### For point A(3, 7):

1. Calculate \( A' \):
\[
A' = (2 \cdot 3, 2 \cdot 7) = (6, 14)
\]

### For point B(4, 9):

1. Calculate \( B' \):
\[
B' = (2 \cdot 4, 2 \cdot 9) = (8, 18)
\]

Thus, the coordinates after dilation are:

- \( A'(6, 14) \)
- \( B'(8, 18) \)

Therefore, the correct response is:

**A′(6,14) and B′(8,18)**.