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 ?

Answer 1

To find the coordinates of point A after a dilation of magnitude 3 with a center of dilation at (3, 0), we can use the following formula for dilating a point \( (x, y) \):

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

where:
- \( (x', y') \) are the coordinates of the dilated point,
- \( (c_x, c_y) \) is the center of dilation,
- \( k \) is the magnitude of the dilation (in this case, \( k = 3 \)),
- \( (x, y) \) are the coordinates of the original point.

Let’s denote the coordinates of point A as \( (x_a, y_a) \). The center of dilation is \( (3, 0) \). Using the values in our formula, we can calculate the new coordinates after dilation.

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

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

Therefore, the corresponding ordered pair to point A after dilation is:

\[
(x', y') = (3x_a - 6, 3y_a)
\]

To finalize the answer, we need the original coordinates \( (x_a, y_a) \) of point A, which are not provided in the question. If you provide those coordinates, I can give you the exact coordinates after dilation.