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′(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′(−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′(32,72)
and B′(2,92)

Answer 1

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

\[
A' = (k \cdot x_A, k \cdot y_A)
\]
\[
B' = (k \cdot x_B, k \cdot y_B)
\]

where \( k \) is the scale factor, and \( (x_A, y_A) \) and \( (x_B, y_B) \) are the coordinates of points \( A \) and \( B \).

Given:
- \( A(3, 7) \)
- \( B(4, 9) \)
- Scale factor \( k = 2 \)

Calculating the coordinates:

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

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

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

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