Question

show that A(5,6) , B(1,5), C(2,1) and D(6,2) are the vertices of a square

Answer 1

Distance Formula

→ √[(x₂ - x₁)² + (y₂ - y₁)²]

Proof

AB = √[(5 - 1)² + (6 - 5)²] = √17

BC = √[(2 - 1)² + (1 - 5)²] = √17

CD = √[(6 - 2)² + (2 - 1)²] = √17

AD = √[(6 - 5)² + (2 - 6)²] = √17

Hence all sides of this quadrilateral are equal.

Let's see whether it's diagonal are equal or not,

AC = √[(5 - 2)² + (6 - 1)²] = √34

BD = √[(6 - 1)² + (2 - 5)²] = √34

Hence diagonals of this quadrilateral are also equal.

Thus, out of every quadrilateral only Sqaure can have equal sides snd diagonals.

Therefore this quadrilateral is Square.

Q.E.D