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

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) Distance between$(2,3)$ and $(4,1)$ is

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

$=\sqrt{(-2{)}^2+(2{)}^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}$

(ii) Distance between $(-5,7)$ and $(-1,3)$ is

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

$=\sqrt{(-4{)}^2+(4{)}^2}=\sqrt{16+16}=\sqrt{32}=4\sqrt{2}$

(iii )Distance between $(a,b)$ and$(-a,-b)$ is

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

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