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.

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  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.

hello from mrbilldoesmath!

answer:

x - 3

discussion:

x^2 - 9 = (x-3) (x+3)   so

(x^2-9)/ (x + 3) = x-3

you,

mrb

step-by-step explanation:

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