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.

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.