Question

Find the dilation of 1/3 for the given shape centered at the origin.
the ponits are
(3,0)
(9,0)
(6,9)

Answer 1

To find the dilation of a shape centered at the origin, we multiply each coordinate of the points by the dilation factor.

Given the dilation factor of \( \frac{1}{3} \) and the points:

1. \( (3, 0) \)
2. \( (9, 0) \)
3. \( (6, 9) \)

We apply the dilation as follows:

1. For the point \( (3, 0) \):
\[
\left(\frac{1}{3} \cdot 3, \frac{1}{3} \cdot 0\right) = (1, 0)
\]

2. For the point \( (9, 0) \):
\[
\left(\frac{1}{3} \cdot 9, \frac{1}{3} \cdot 0\right) = (3, 0)
\]

3. For the point \( (6, 9) \):
\[
\left(\frac{1}{3} \cdot 6, \frac{1}{3} \cdot 9\right) = (2, 3)
\]

Thus, after applying the dilation of \( \frac{1}{3} \), the new coordinates are:

1. \( (1, 0) \)
2. \( (3, 0) \)
3. \( (2, 3) \)

These points represent the dilated shape centered at the origin.