Question

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

Answer 1

The formula for the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\).

(i) The distance between (2, 3) and (4, 1) is calculated as follows:

\(l=\sqrt{(2-4)^2+(3-1)^2}\)
\(l=\sqrt{(-2)^2+(2)^2}\)
\(l=\sqrt{4+4}\)
\(l=\sqrt8\)
\(l=2\sqrt2\)

---

(ii) The distance between (– 5, 7) and (– 1, 3) is calculated as follows:

\(l=\sqrt{(-5-(-1))^2+(7-3)^2}\)
\(l=\sqrt{(-4)^2+(4)^2}\)
\(l=\sqrt{16+16}\)
\(l=\sqrt{32}\)
\(l=4\sqrt2\)

---

(iii) The distance between (a, b) and (– a, – b) is calculated as follows:

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