Question

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

Answer 1

Given, points A(5,6), B(1,5) C(2,1) and D(6,2).
By applying Distance Formula,
AB = √(1-5)² + (5-6)² = √17 units
BC = √(2-1)² + (1-5)² = √17 units
CD = √(6-2)² + (2-1)² = √17 units
AD = √(6-5)² + (2-6)² = √17 units
Clearly, AB=BC=CD=AD→(1)
Also, AC = √(2-5)² + (1-6)² = √34 units
BD = √(6-1)² + (2-5)² = √34 units
∴ AC=BD→(2)
From (1) and (2), we can conclude,
ABCD is a square.