Question

rectangle ABCD is drawn on a coordinate plane. If the rectangle were dilated using a magnitude of 3 and center of dilation at (3,0). What would be the corresponding ordered pair to point A

A is 0,0

Answer 1

To find the coordinates of the dilated point A, we can use the formula for dilation with a center of dilation at point \(C(x_c, y_c)\) and a magnitude of \(k\):

\[
A' = (x_c + k(x_a - x_c), y_c + k(y_a - y_c))
\]

Where:
- \(A(x_a, y_a)\) is the original point.
- \(C(x_c, y_c)\) is the center of dilation.
- \(k\) is the magnitude of the dilation.

For your case:
- Point A is \((0, 0)\) (i.e., \(x_a = 0\) and \(y_a = 0\)).
- The center of dilation is \((3, 0)\) (i.e., \(x_c = 3\) and \(y_c = 0\)).
- The magnitude of the dilation is \(3\) (i.e., \(k = 3\)).

Now, substituting these values into the dilation formula:

1. Calculate the new x-coordinate:
\[
x' = 3 + 3(0 - 3) = 3 + 3(-3) = 3 - 9 = -6
\]

2. Calculate the new y-coordinate:
\[
y' = 0 + 3(0 - 0) = 0 + 3(0) = 0 + 0 = 0
\]

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

\[
A' = (-6, 0)
\]