Use the image to answer the question.

Question

A coordinate plane's axes range from negative 1 to 4 by 1-unit increments. 4 points forming a rectangle are plotted. They are labeled upper A, upper B, upper C, and upper D, respectively.

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
?

(1 point)
The new ordered pair for point D′
would be at (
,
).

Answer 1

To find the new coordinates for point D after a dilation with a center of dilation at (1,1) and a magnitude of 12, we can use the following formula for dilation:

\[ D' = \left( x_c + m(x - x_c), y_c + m(y - y_c) \right) \]

Where:

• \((x_c, y_c)\) is the center of dilation, which in this case is (1, 1).
• \(m\) is the magnitude of dilation, which is 12.
• \((x, y)\) are the original coordinates of point D.

Unfortunately, I do not have access to the actual coordinates of point D since the image is not provided. However, you can follow these steps:

1. Substitute the coordinates of point D into the equation.
2. Substitute the center of dilation and the magnitude into the equation.
3. Calculate the new coordinates.

For example, if point D had original coordinates \((x,y)\), you would compute:

\[ D' = \left( 1 + 12(x - 1), 1 + 12(y - 1) \right) \]

Calculate each component to find the new coordinates. Once you provide the original coordinates of point D, I can assist you with the specific calculation.