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)
.

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)

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 use the following formula for dilation:

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

where \( (x, y) \) are the original coordinates, \( (x', y') \) are the new coordinates after dilation, and \( k \) is the scale factor.

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

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

**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 answer is:
**A′(6,14) and B′(8,18)**.