Question

The distance between the points (a, b) and (–a, –b) is

(a) 0

(b) 1

(c) \(\sqrt{ab}\)

(d) \(2\sqrt{a^2 + b^2}\)

Answer 1

Correct option is (d) \(2\sqrt{a^2 + b^2}\)

Distance between two points (x₁​, y_1​) and (x₂​, y₂​) can be calculated using the formula \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Therefore, distance between the points (a, b) and (−a, −b) is

\(= \sqrt{(-a-a)^2 + (-b-b)^2}\)

\(= \sqrt{4a^2 + 4b^2}\)

\(= 2\sqrt{a^2 + b^2}\)