Question

Suppose a parallelogram on the coordinate plane is dilated in reference to the origin using a magnitude of 3. What would the coordinates be of the new vertex A'
Coordinate A is at (-1,3)
Coordinate B is at (2,6)
Coordinate C is at (5,2)
Coordinate D is at (1,1)

Answer 1

To find the new coordinates of vertex A' after dilating the point A at (-1, 3) from the origin with a scale factor of 3, you can use the following formula for dilation:

\[
A' = (kx, ky)
\]

where \( k \) is the scale factor, and \( (x, y) \) are the original coordinates.

For vertex A at (-1, 3):

1. \( k = 3 \)
2. Original coordinates \( (x, y) = (-1, 3) \)

Now apply the formula:

\[
A' = (3 \cdot -1, 3 \cdot 3) = (-3, 9)
\]

Thus, the new coordinates of vertex A' after dilation are \( (-3, 9) \).

You can apply the same process to find the new coordinates of the other vertices B, C, and D if desired.

- For B(2, 6):
\[
B' = (3 \cdot 2, 3 \cdot 6) = (6, 18)
\]

- For C(5, 2):
\[
C' = (3 \cdot 5, 3 \cdot 2) = (15, 6)
\]

- For D(1, 1):
\[
D' = (3 \cdot 1, 3 \cdot 1) = (3, 3)
\]

Thus, the new coordinates after dilation will be:
- \( A' = (-3, 9) \)
- \( B' = (6, 18) \)
- \( C' = (15, 6) \)
- \( D' = (3, 3) \)