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