# ABCD is a parallelogram whose vertices are (-3,2), (1,5) and (2,-4) respectively, then the coordinates of fourth vertex is

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parrallel lines have same slope

slope of AB=Slope of CD

solve it 3x-4y-22=0....(1)

slope of AD=slope of BC

solve it 9x+y+25=0....(2)

solve

(1) and (2) we get x=-2 ,y=-7

the fourth vertex is (-2,-7)

A(-3,2), B(1,5), C(2,-4) and D(x,y)

((-3+2)/2,(2-4)/2) = ((1+x)/2,(5+y)/2)

(-1/2,-2/2) = ((x+1)/2,(y+5)/2)

(-1/2,-1) = ((x+1)/2,(y+5)/2)

(x+1)/2 = -1/2, (y+5)/2 = -1

Therefore x = -2 and y =-7

The fourth vertices is (-2,-7)