Question

Find the dilation of 1/3
for the given shape centered at the origin.

a=3,0
b=9,0
c=6,9

Answer 1

To find the dilation of a shape centered at the origin by a scale factor of \(\frac{1}{3}\), we multiply each coordinate of the shape by the dilation factor.

Given the points:
- \( A(3, 0) \)
- \( B(9, 0) \)
- \( C(6, 9) \)

We perform the dilation for each point as follows:

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

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

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

Thus, the coordinates of the dilated shape are:
- \( A'(1, 0) \)
- \( B'(3, 0) \)
- \( C'(2, 3) \)

These are the points of the shape after applying the dilation of \(\frac{1}{3}\).