Coordinate Geometry-20

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Find the value of x₁ if the distance between the points (x₁, 2) and (3, 4) be 8.

Solution: Square of the distance between the points (x₁, 2) and (3, 4) = (x₁ - 3)² + (2 - 4)² = 8²

(x₁ - 3)² + 4 = 64

(x₁ - 3)² = 60

(x₁ - 3) = √(4 x 15)

Therefore, (x₁ - 3) = ± 2 √15;

Therefore, x₁ = 3 ± 2 √15