Question

verify the following points taken in order form the vertices of a rhombus. A(1,1),B(2,1),C(2,2),D(1,2)

Answer 1

A(1,1),B(2,1),C(2,2),D(1,2)

XY= √(x2- x1)² + (y2- y1)² )

AB=√ ((2-1)²+ (1-1)²

= √(1)

AB= 1

BC= √2-2)²+ (2-1)²

 = √1

BC= 1

CD= √(1-2)²+ (2-2)²

CD= 1

AD= √(1-1)²+(2-1)²

AD = 1

∴ AB=BC=CD=AD

AC=√(2-1)²+ (2-1)²

    AC=√2

BD=√(1-2)²+(2-1)²

 BD= √2

∴AC=BD

As all the sides are equal and diagonals are equal

its shows that the following vertices are of a square

It is a special rhombus whose angle is 90 degree.