Question

Find the dilation of 1/2 for the given shape centered at the origin.
a=(2,2)
b=(0,8)
c=(4,-6)

Answer 1

To find the dilation of a shape centered at the origin with a scale factor of \( \frac{1}{2} \), you multiply each coordinate of the points by the scale factor.

Given the points:

- \( a = (2, 2) \)
- \( b = (0, 8) \)
- \( c = (4, -6) \)

We apply the dilation transformation \( (x, y) \rightarrow \left( \frac{1}{2}x, \frac{1}{2}y \right) \).

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

2. For point \( b = (0, 8) \):
\[
b' = \left( \frac{1}{2} \times 0, \frac{1}{2} \times 8 \right) = (0, 4)
\]

3. For point \( c = (4, -6) \):
\[
c' = \left( \frac{1}{2} \times 4, \frac{1}{2} \times -6 \right) = (2, -3)
\]

Thus, the dilated points are:
- \( a' = (1, 1) \)
- \( b' = (0, 4) \)
- \( c' = (2, -3) \)

In summary, after performing the dilation by a factor of \( \frac{1}{2} \) centered at the origin, the new coordinates of the points are:
- \( a' = (1, 1) \)
- \( b' = (0, 4) \)
- \( c' = (2, -3) \)