HELP A polygon has vertices whose coordinates are A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1). Use the midpoint formula to determine whether or not the diagonals of polygon ABCD bisect each other. In your final answer, include all of your calculations.

9514 1404 393

  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.

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.