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 distance between two points (D) is given by distance formula as

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

$\left(i\right)$ D $=\sqrt{(4-2{)}^2+(1-3{)}^2}=\sqrt{4+4}=2\sqrt{2}$ units

$\left(ii\right)$ D $=\sqrt{(-5+1{)}^2+(7-3{)}^2}=\sqrt{16+16}=4\sqrt{2}$ units

$\left(iii\right)$ D $=\sqrt{(a+a{)}^2+(b+b{)}^2}=2\sqrt{a^2+b^2}$ units