Question

d ( 3,3)
Suppose you dilate the rectangle on the coordinate plane using a magnitude of 12 and the center of dilation at (1,1) . What would be the corresponding ordered pair to the current point D ?

Answer 1

To perform a dilation of a point \( D(3, 3) \) using a center of dilation at \( (1, 1) \) and a magnitude of 12, you can use the formula for dilation.

The formula for the coordinates \( (x', y') \) of the dilated point is given by:

\[
(x', y') = (x_c + k(x - x_c), y_c + k(y - y_c))
\]

where:
- \( (x_c, y_c) \) is the center of dilation,
- \( (x, y) \) is the original point,
- \( k \) is the dilation factor (magnitude).

In this case:
- \( (x_c, y_c) = (1, 1) \)
- \( (x, y) = (3, 3) \)
- \( k = 12 \)

Plugging in the values:

1. For \( x' \):
\[
x' = 1 + 12(3 - 1) = 1 + 12(2) = 1 + 24 = 25
\]

2. For \( y' \):
\[
y' = 1 + 12(3 - 1) = 1 + 12(2) = 1 + 24 = 25
\]

Thus, the new coordinates after dilation are \( (25, 25) \).

So, the corresponding ordered pair to the current point \( D \) after dilation is \( (25, 25) \).