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′(−6,3) 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 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′(6,14) and B′(−4,3)

Answer 1

To perform a dilation of a point \((x, y)\) centered at the origin with a scale factor \(k\), you use the formula:
\[
(x', y') = (kx, ky)
\]

For point \(A(3, 7)\):
- Dilation with scale factor 2:
\[
A' = (2 \cdot 3, 2 \cdot 7) = (6, 14)
\]

For point \(B(4, 9)\):
- Dilation with scale factor 2:
\[
B' = (2 \cdot 4, 2 \cdot 9) = (8, 18)
\]

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

Therefore, the correct response is:
**A′(6,14) and B′(8,18)**.