Apolygon 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. now

Yes, They do Bisect Eachother.

For a polygon ABCD, the diagonals are AC and BD.
The midpoint formulas are:
x M = ( x 1 + x 2 )/2    and   y M = ( y 1 + y 2 ) / 2
For AC:
x M = ( x A + x C ) / 2 = ( 1 + ( - 1 ) ) / 2 = 0
y M = ( y A + y C ) / 2 = ( 4 + ( - 4 ) ) / 2 = 0
Therefore: M ( 0, 0 ) - the midpoint of the diagonal AC.
For BD:
x M = ( x B + x D ) / 2  = ( 4 + ( - 4 ) ) / 2  = 0
y M = ( y B + y D ) / 2 = ( - 1 + 1 ) / 2 = 0
M ( 0, 0 ).
Because the midpoint of the both diagonals is the same ( 0, 0 ), we cam say that the diagonals of polygon ABCD bisect each other.