9514 1404 393
Answer:
the diagonals bisect each other
Step-by-step explanation:
The midpoint formula tells you the midpoint M of segment XY is ...
M = (X + Y)/2
In your problem, the diagonals will bisect each other if they have the same midpoint. That is, we want to see if ...
(A +C)/2 = (B +D)/2
Multiplying by 2 can simplify our work a bit. In short, we want to test ...
A +C = B +D
(1, 4) +(-1, -4) = (4, -1) +(-4, 1) . . . . fill in the point coordinates
(1-1, 4-4) = (4-4, -1+1) . . . . . . . . . . simplify a bit
(0, 0) = (0, 0) . . . . . . . true, the midpoints are the same
The diagonals are mutual bisectors.
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