Distance formula to find the distance between two points (x₁, y₁) and (x₂, y₂) is, say d

d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

or d = \(\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

(i) Distance between (2, 3), (4, 1)

d = \(\sqrt{(4 - 2)^2 + (1-3)^2}\)

= \(\sqrt{(2)^2 + (-2)^2}\) = \(\sqrt{8}\)

= \(2\sqrt{2}\)

(ii) Distance between (-5, 7), (-1, 3)

d = \(\sqrt{(-1 + 5)^2 + (3-7)^2}\)

= \(\sqrt{(4)^2 + (-4)^2}\) = \(\sqrt{32}\)

= \(4\sqrt{2}\)

(iii) Distance between (a, b), (- a, – b)

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

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

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