Find the distance between the following pairs of points:
(i) (2, 3), (4, 1)
(ii) (-5, 7), (-1, 3)
(iii) (a, b), (- a, – b)

Distance formula =\(\sqrt { (x_2 - x_1)^2 + (y_2 - y_1)^2}\)
(i) Applying Distance Formula to find distance between points (2, 3) and (4,1), we get
d = \(\sqrt { (4 - 2)^2 + (1 - 3)^2} \)
\( = \sqrt{ 2^2 + (-2) ^2} = \sqrt{4 + 4} \)
\( = \sqrt{8} \)
\( = 2\sqrt{2}\)

(ii) Applying Distance Formula to find distance between points (–5, 7) and (–1, 3), we get
d = \(\sqrt { (-5 + 1)^2 + (7 - 3)^2} \)
\( = \sqrt{ ((-4)^2 + (4) ^2} = \sqrt{16 + 16} \)
\( = \sqrt{32} \)
\( = 4\sqrt{2}\)

(iii) Applying Distance Formula to find distance between points (a, b) and (–a, –b), we get
d = \(\sqrt { (-a - a)^2 + (-b - b)^2} \)
\( = \sqrt{ ((-2a)^2 + (-2b) ^2} \)
\( = \sqrt{4a^2 + 4b^2} \)
\(= 2\sqrt{a^2 + b^2}\)