The coordinates of the center of dilation for this transformation are: A. (-5, 1).
In this exercise, we would have to dilate the coordinates of the preimage by using a scale factor of 2 centered at a point (a, b) by using this mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
Based on the coordinates of the image P' (3, 1), we have;
P' (3, 1) → (2(3 - a) + a, 2(1 - b) + b)
P' (3, 1) = (6 - 2a + a, 2 - 2b + b)
P' (3, 1) = (-6 - a, 2 - b)
Next, we would set up a system of equations from the above with respect to the pre-image P (-1, 1);
-1 = -6 - a
a = -6 + 1
a = -5
1 = 2 - b
b = 2 - 1
b = 1
Therefore, the coordinates of the center of dilation are (-5, 1).
Missing information:
Triangle MNP is dilated by a scale factor of 2, resulting in triangle M'N'P'.
What are the coordinates of the center of dilation for this transformation? (-5,1)
(-3,0)
(-1,1)
(0,0).