A triangle on a coordinate plane has three vertices A(2 , 3), B(5, 4), and C(3, 6). Use this description to do the following transformations (if needed, draw this triangle on a sheet of paper):

a. Dilation 1: What would be the new coordinates if this triangle were dilated to a scale factor of 2 with the center of the dilation at the origin? How did you determine these points?
b. Dilation 2: What would be the new coordinates if this triangle were dilated to a scale factor of 2 with the center of the dilation at the point P(6, 8)? How did you determine these points?
c. What series of transformations would carry dilation 1 onto dilation 2? Compare Dilation 1 to Dilation 2. Explain what conclusions you can draw about the scale factor, difference in area, and center of dilation.
d. What is the proportion of the side lengths from Dilation 1 to Dilation 2? What is the proportion of their angle measures? Explain your answer.