Question

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

Answer 1

(i) Distance between the points is given by
$\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$
Therefore, the distance between (2,3) and (4,1) is given by
$l=\sqrt{{(2-4)}^2+{(3-1)}^2}$
$=\sqrt{{(-2)}^2+{\left(2\right)}^2}$
$=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}$

(ii) Distance between the points is given by
$\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$
Therfore distance between (−5, 7) and (−1, 3) is given by
$l=\sqrt{{(-5-(-1))}^2+{(7-3)}^2}$
$=\sqrt{{(-4)}^2+{\left(4\right)}^2}$
$=\sqrt{16+16}=\sqrt{32}=4\sqrt{2}$