Question

Find the dilation of 2 for the given shape centered at the origin
a=1,4
b=1,1
c=3,1
d=3,4

Answer 1

To find the dilation of a shape centered at the origin with a scale factor of 2, we will multiply each coordinate of the vertices by 2.

Given the points of the shape:
- \( a = (1, 4) \)
- \( b = (1, 1) \)
- \( c = (3, 1) \)
- \( d = (3, 4) \)

We apply the dilation formula for each point, which involves multiplying each coordinate by the dilation factor (2):

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

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

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

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

Thus, the dilated points are:
- \( a' = (2, 8) \)
- \( b' = (2, 2) \)
- \( c' = (6, 2) \)
- \( d' = (6, 8) \)

Therefore, the coordinates of the dilated shape are:
- \( (2, 8) \)
- \( (2, 2) \)
- \( (6, 2) \)
- \( (6, 8) \)