Sum

A(−1, 1), B(1, 3) and C(3, a) are point and if AB = BC, then find ‘a’

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#### Solution

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

AB = `sqrt((1 + 1)^2 + (3 - 1)^2`

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

= `sqrt(4 + 4)`

= `sqrt(8)`

BC = `sqrt((3 - 1)^2 + ("a" - 3)^2`

= `sqrt((2)^2 + ("a" - 3)^2`

= `sqrt(4 + ("a" - 3)^2`

But given AB = BC

⇒ `sqrt(8) = sqrt(4 + ("a" - 3)^2`

4 + (a – 3)^{2} = 8

(a – 3)^{2} = 8 – 4

(a – 3)^{2} = 4

a – 3 = `sqrt(4)`

= ± 2

a – 3 = 2 or a – 3 = – 2

a = 2 + 3 or a = 3 – 2

a = 5 or a = 1

∴ The value of a = 5 or a = 1.

Concept: Co-ordinates of Points and Distance

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