Question

Select the coordinates A' and B after dilation of the line segment AB with a scale factor of ⅓, centered at the origin where the endpoints are A(-6,3) and B(-12,9). (1 point)

A(-2,1) and B (-4,3)

A'(-6,3) and B (-4,3)

A(-18,9) and B (-36,27)

A(-2,1) and B (-12,9)

Answer 1

To find the coordinates of the points A' and B after dilation, we can use the formula for dilation centered at the origin, which is given by:

\[
(x', y') = (k \cdot x, k \cdot y)
\]

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

Given that the scale factor \( k = \frac{1}{3} \), we can calculate the new coordinates for points A and B.

1. For point A(-6, 3):
\[
A' = \left(\frac{1}{3} \cdot (-6), \frac{1}{3} \cdot 3\right) = \left(-2, 1\right)
\]

2. For point B(-12, 9):
\[
B' = \left(\frac{1}{3} \cdot (-12), \frac{1}{3} \cdot 9\right) = \left(-4, 3\right)
\]

Thus, the coordinates after dilation are:
\[
A'(-2, 1) \quad \text{and} \quad B'(-4, 3)
\]

Therefore, the correct answer is:
**A'(-2, 1) and B'(-4, 3)**.