Graph the points A(13,7), B(9,1), C(3,5), and D(7,11). Connect the points to create a quadrilateral. Are the diagonals of the figure are perpendicular bisectors of each other? Explain

Answer 1

If the quadrilateral has all four sides of equal length, then it will be a rhombus.

If the quadrilateral is a rhombus then the diagonals will be perpendicular..

Thus we need to determine the length of all 4 sides using the distance formula.

If you do so you will find that the length of each of all four sides = SQRT(52) = 7.2

Thus the quadrilateral is a rhombus and the diagonals are perpendicular.

A rhombus is a parallelogram, for which the diagonals bisect each other.

Therefore, the diagonals are perpendicular bisectors of each other.