Triangle abc, with coordinates a(2,3), b(3,5), c(7,4), is dilated by a scale factor of 2. what are the coordinates of the dilated figure, triangle a’b’c’?

Answer is choice C

"Dilate with a scale factor of two" means "multiply each coordinate by two"
A = (2,3) turns into A' = (4,6)
B = (3,5) turns into B' = (6,10)
C = (7,4) turns into C' = (14,8)

Side Note: this quick shortcut only works if the center of dilation is the origin (0,0). If the center of dilation isn't the origin, then you will have to do a translation (shifting) before you can use the trick, and then you'll have to shift back. The idea of the shifting is so that the center of dilation becomes the origin on a temporary basis. Because no mention is made of the reference center, it is assumed to be the origin by default.