Question

what are the coordinates of the center of dilation for the dilation shown?
the center of dilation is
(type an ordered pair.)

Explanation:

Step1: Recall the definition of the center of dilation

The center of dilation is the fixed point about which all points are expanded or contracted. In a coordinate - plane, for a dilation of a figure, we can find the center by looking for the point that is common to both the original figure and its dilated image.

Step2: Analyze the given figures

Looking at the two figures (the black and the red one), we can observe that the \(x\) - coordinate of the center of dilation can be found by looking at the horizontal alignment. The \(y\) - coordinate is found by vertical alignment.
For the \(x\) - coordinate:
If we consider the horizontal position, we can see that the center of dilation has an \(x\) - value of \(8\).
For the \(y\) - coordinate:
If we consider the vertical position, we can see that the center of dilation has a \(y\) - value of \(12\).

Answer:

\((8,12)\)