Abcd is a parallelogram with an and c diagonally opposite. the coordinates of a, b and c are (-3, -2), (1,-5), and (9,1) respectively. the sum of the coordinates of point d is

Check the picture below.

in a parallelogram, there are two pairs of parallel sides, so in this case, namely since A and C are on opposite ends of the diagonal, that means that the segment AB is the one that's parallel to CD, and of course, AD is parallel to BC.

in order to maintain the same "slant" or slope, that way the sides are indeed parallel, since parallel sides have the same slant, we can just check how much is it horizontally from B to C, and then how much is it from there up to C, vertically.

if we move the same quantities horizontally and vertically, from A, we will end up at D, while maintaning the slant.

so... notice in the picture the blue distances from B up to C, we move that much in the red distances from A up to D.

what are the coordinates of D?  well, ok, add them up.

Main idea on left, details on right