Question

Rectangle ABCD is dilated by a scale factor of One-half with a center of dilation at the origin. What are the coordinates of the image of point B prime?

On a coordinate plane, rectangle A B C D has points (negative 8, 6), (negative 4, 6), (negative 4, 4), (negative 8, 4).


(–2, 3)
(3, –2)
(–8, 12)
(12, –8)

Answer 1

To find the coordinates of point B' (the image of point B) after dilation, we need to apply the scale factor to the coordinates of point B.

Given:
- The coordinates of point B are (-4, 6).
- The scale factor is \( \frac{1}{2} \), and the center of dilation is at the origin (0, 0).

To find the new coordinates, we apply the formula for dilation:
\[
(x', y') = (kx, ky)
\]
where \( k \) is the scale factor, and \( (x, y) \) are the original coordinates.

Substituting the values:
\[
x' = \frac{1}{2} \cdot (-4) = -2
\]
\[
y' = \frac{1}{2} \cdot (6) = 3
\]

Thus, the coordinates of point B', after dilation, are (-2, 3).

So, the answer is **(–2, 3)**.