Question

A triangle has vertices A(3,4), B(2,2) and C(4,2). Its dilated figure has vertices A'(5,5), B'(3,1) and C'(7,1). Using formula, find center of dilation.

note: I do not know formula to find center of dilation. Please let me know.

Answer 1

I don't know the formula but this link will help you

http://regentsprep.org/Regents/math/geometry/GT3/Ldilate2.htm

Answer 2

from the above link, you should find that the new coordinates are found by multiplying scale factor k by the distance from center of dilation.
set up some equations
k*|x-3| = 5
k*|y-4| = 5
k*|x-2| = 3
k*|y-2| = 1
you dont even need point C
now you can solve for center (x,y) and k