Question

Find the dilation of 2 for the given shape centered at the origin.
the ponts are
(1,4)
(1,1)
(3,1)
(3,4)

Answer 1

To perform a dilation of a shape centered at the origin by a factor of 2, you simply multiply the coordinates of each point by the dilation factor.

Given the points:
- (1, 4)
- (1, 1)
- (3, 1)
- (3, 4)

Now, let's apply the dilation factor of 2 to each point:

1. For the point (1, 4):
\[
(1 \cdot 2, 4 \cdot 2) = (2, 8)
\]

2. For the point (1, 1):
\[
(1 \cdot 2, 1 \cdot 2) = (2, 2)
\]

3. For the point (3, 1):
\[
(3 \cdot 2, 1 \cdot 2) = (6, 2)
\]

4. For the point (3, 4):
\[
(3 \cdot 2, 4 \cdot 2) = (6, 8)
\]

Now, the new points after dilation are:
- (2, 8)
- (2, 2)
- (6, 2)
- (6, 8)

So, the dilated points are:
**(2, 8), (2, 2), (6, 2), (6, 8)**.