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′(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′(32,72)
and B′(2,92)

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 can apply the following formula for dilation:

If \( (x, y) \) is a point, then after dilation with a scale factor \(k\) centered at the origin, the new coordinates \( (x', y') \) are given by:

\[
(x', y') = (kx, ky)
\]

Given \(A(3, 7)\) and \(B(4, 9)\) and the scale factor of \(2\):

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

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

So the \(A'\) and \(B'\) coordinates after dilation are \(A'(6, 14)\) and \(B'(8, 18)\).

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