Question

Points r(-4,-1) and s(6,3) are the endpoints of a diagonal of a rhombus. find the equation of the line containing the other diagonal.

Answer 1

Note that he diagonals of a rhombus are perpendicular bisectors of each other.

slope = (3+1)/(6+4) = 4/10 = 2/5
the other diagonal slope = -5/2

midpoint of the diagonal is where the two diagonals meet. 
midpoint ((-4+6)/2, (-1+3)/2) = (1, 1)

equation of the other diagonal line:
y = mx + c
y = -5/2 x + c
at (1,1)
1 = -5/2(1) + c
c = 1 + 5/2 = 7/2

y = -5/2 x + 7/2
2y = -5x + 7