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

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:

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