Question

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

Answers

A’ (-2,1) and B’ (-4,3)

A’ (-18,9) and B’ (-36,27)

A’ (-6,3) and B’ (-4,3)

A’ (-2,1) and B’ (-12,9)

Answer 1

To find the coordinates of A’ and B’ after dilating the line segment AB with a scale factor of \( \frac{1}{3} \) from the origin, you can use the formula for dilation:

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

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

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

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

After the dilation, the coordinates of point A’ are (-2, 1) and point B’ are (-4, 3).

Thus, the correct answer is:

A’ (-2, 1) and B’ (-4, 3).