Sum

Verify that the following points taken in order to form the vertices of a rhombus

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

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#### Solution

Distance = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

AB = `sqrt((2 - 1)^2 + (1 - 1)^2`

= `sqrt((1)^2 + (0)^2`

= `sqrt(1)`

= 1

BC = `sqrt((2 - 2)^2 + (2 - 1)^2`

= `sqrt((0)^2 + (1)^2`

= `sqrt(1)`

= 1

CD = `sqrt((1 - 2)^2 + (2 - 2)^2`

= `sqrt((- 1)^2 + (0)^2`

= `sqrt(1)`

= 1

AD = `sqrt((1 - 1)^2 + (2 - 1)^2`

= `sqrt((0)^2 + (1)^2`

= `sqrt(1)`

= 1

AB = BC = CD = AD = 1.

All the four sides are equal.

∴ ABCD is a rhombus.

Concept: Co-ordinates of Points and Distance

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