Question

prove that the diagonals of a rectangle with vertices(0,0), (a,0), (a,b) and (0,b) bisect each other are equal

Answer 1

let A (0,0) B (a,0) C (a, b) and D (0, b)
here AC and BD is diagonal of rectangle .
midpoint of AC
use section formula
{(0+a)/2, (0+b)/2}=(a/2, b/2)

also find midpoint of BC
{(a+0)/2,(0+b)/2}=(a/2, b/2)

we see
midpoint of AC =midpoint of BD
hence midpoint of both diagonals meet at a same point (a/2, b/2)
so, we can say that diagonals of a rectangle bisect each other are equal.

Answer 2

Here, we use distance formula to prove that the diagonals are equal and mid-point formula to prove that they bisect each other.

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Hope it helps...