Question

Quadrilateral ABCD with vertices A(4, 3), B(4, -2), C(-4, -2) and D(-4, 3) is a rectangle, find the length of the diagonals

Answer 1

Quadrilateral ABCD with vertices A(4, 3), B(4, -2), C(-4, -2) and D(-4, 3) is a rectangle, find the length of the diagonals.

Diagonals of quadrilateral are AC and BD.

Distance between points with coordinates $(x_{1},y_{1})$ and $(x_{2},y_{2})$ equals:

$$d = \sqrt {(x _ {1} - x _ {2}) ^ {2} + (y _ {1} - y _ {2}) ^ {2}}$$

Length of AC equals:

$$A C = \sqrt {\left(4 - (- 4)\right) ^ {2} + \left(3 - (- 2)\right) ^ {2}} = \sqrt {6 4 + 2 5} = \sqrt {8 9}$$

Length of BD equals:

$$B D = \sqrt {\left(4 - (- 4)\right) ^ {2} + \left(3 - (- 2)\right) ^ {2}} = \sqrt {6 4 + 2 5} = \sqrt {8 9}$$

Answer: $\sqrt{89}$