Question

Prove that the diagonals of a rectangle ABCD with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6) are equal and bisect each other.

Answer 1

Vertices f a rectangle ABCD are A(2, -1), B(5, -1), C(5, 6) and D(2, 6)

To prove: Diagonals of the rectangle are equal and bisect each other.

AC and BD are equal in length. Thus, Diagonals are equal.

Now,

Consider that O is the midpoint of AC then its coordinates are Midpoint formula:

If point O divides AC in the ratio m:n then,

7/2 = (mx₂ + nx₁)/ (m + n) = (m x 2 + n x 5)/(m + n)

2m + 5n/ m + n

7m + 7n = 4 m + 10n

7m - 4m = 10n - 7n

3m = 3n

m = n

Which shows, O is the midpoint of diagonals.