Question

Suppose parralelogram ABCD is dilated using a magnitude of 2 and a center of dilation at (-2,-1) What would be the corresponding ordered pair at point A

Answer 1

To find the corresponding ordered pair at point \( A \) after the dilation of parallelogram \( ABCD \), we will use the dilation formula.

The formula for a point \( (x, y) \) that is dilated from a center of dilation \( (c_x, c_y) \) with a scale factor \( k \) is given by:

\[
(x', y') = (c_x + k \cdot (x - c_x), c_y + k \cdot (y - c_y))
\]

Given:
- Center of dilation \( (-2, -1) \)
- Scale factor \( k = 2 \)
- Original coordinates of point \( A \) (let's denote them as \( (x_A, y_A) \))

For the purpose of this calculation, let's denote the coordinates of point \( A \) as \( (x_A, y_A) \). We will apply the dilation formula to this point.

Substituting in the values, the new coordinates \( (x', y') \) will be:

\[
x' = -2 + 2 \cdot (x_A + 2)
\]

\[
y' = -1 + 2 \cdot (y_A + 1)
\]

This yields:

\[
x' = -2 + 2x_A + 4 = 2x_A + 2
\]

\[
y' = -1 + 2y_A + 2 = 2y_A + 1
\]

Thus, the new coordinates of point \( A \) after dilation will be:

\[
(x_A', y_A') = (2x_A + 2, 2y_A + 1)
\]

If you provide the specific coordinates of point \( A \), I can compute the new coordinates explicitly. Otherwise, the transformation has been defined generically.