Question

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

A′(6,14)
and 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)
and 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′(32,72)
and B′(2,92)
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′(−6,3)
and 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
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Answer 1

To find the coordinates \( A' \) and \( B' \) after dilation of the line segment \( AB \) with a scale factor of 2, centered at the origin, we multiply each coordinate of points \( A \) and \( B \) by the scale factor.

The coordinates of the endpoints are:
- \( A(3, 7) \)
- \( B(4, 9) \)

Now apply the dilation:

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

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

Therefore, after the dilation, the coordinates are:
\[
A'(6, 14) \text{ and } B'(8, 18)
\]

Looking at the provided options, the correct answer is:
**A′(6,14) and B′(8,18)**.