Question

A (-3,1) B(-5,-1) D (1,0) C(-1,-2)
Suppose parallelogram ABCD is dilated using a magnitude of 2 and a center of dilation at (-2,-1). What could be the corresponding ordered pair at point A

Answer 1

To find the corresponding point \( A' \) after a dilation of point \( A (-3, 1) \) with a center of dilation at \( (-2, -1) \) and a magnitude of 2, we can use the formula for dilation:

\[
A' = (1 - k) O + k A
\]

Where:
- \( O \) is the center of dilation
- \( k \) is the scale factor (in this case, \( k = 2 \))
- \( A \) is the original point

Given:
- \( O = (-2, -1) \)
- \( A = (-3, 1) \)
- \( k = 2 \)

Now we can calculate the coordinates of \( A' \):

1. Calculate \( A - O \):
\[
A - O = (-3, 1) - (-2, -1) = (-3 + 2, 1 + 1) = (-1, 2)
\]

2. Scale this vector by \( k = 2 \):
\[
k(A - O) = 2 \cdot (-1, 2) = (-2, 4)
\]

3. Add this to the center of dilation \( O \):
\[
A' = O + k(A - O) = (-2, -1) + (-2, 4) = (-2 - 2, -1 + 4) = (-4, 3)
\]

Thus, the corresponding ordered pair for point \( A \) after the dilation is:

\[
\boxed{(-4, 3)}
\]