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′(−6,3)
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′(32,72)
A
′
(
3
2
,
7
2
)
and B′(2,92)
B
′
(
2
,
9
2
)
upper A prime left parenthesis Start Fraction 3 over 2 End Fraction comma Start Fraction 7 over 2 End Fraction right parenthesis and upper B prime left parenthesis 2 comma Start Fraction 9 over 2 End Fraction 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′(6,14)
A
′
(
6
,
14
)
and B′(8,18)

Answer 1

To find the coordinates after dilation with a scale factor of 2, centered at the origin, we can use the formula for dilation. The new coordinates \((x', y')\) of a point \((x, y)\) after dilation can be given by:

\[
x' = k \cdot x
\]
\[
y' = k \cdot y
\]

where \(k\) is the scale factor.

Given the points:
- \(A(3, 7)\)
- \(B(4, 9)\)

Let's apply the scale factor \(k = 2\):

For point \(A(3, 7)\):
\[
A'(x', y') = (2 \cdot 3, 2 \cdot 7) = (6, 14)
\]

For point \(B(4, 9)\):
\[
B'(x', y') = (2 \cdot 4, 2 \cdot 9) = (8, 18)
\]

Thus, after dilation, the coordinates are:
- \(A'(6, 14)\)
- \(B'(8, 18)\)

The correct response from the choices you provided is:
**A′(6, 14) and B′(8, 18).**