Question

The distance between the points $(\frac{1}{2},\frac{3}{2})$ and $(\frac{3}{2},\frac{-1}{2})$ is

Answer 1

Let $A(x_1,y_1)=(\frac{1}{2},\frac{3}{2})$ and $B(x_2,y_2)=(\frac{3}{2},\frac{-1}{2})$

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

$\therefore AB=\sqrt{{(\frac{3}{2}-\frac{1}{2})}^2+{(\frac{-1}{2}-\frac{3}{2})}^2}$

$=\sqrt{{\left(\frac{3-1}{2}\right)}^2+{\left(\frac{-1-3}{2}\right)}^2}$

$=\sqrt{{\left(\frac{2}{2}\right)}^2+{\left(\frac{-4}{2}\right)}^2}$

$=\sqrt{{\left(1\right)}^2+{(-2)}^2}$

$=\sqrt{1+4}=\sqrt{5}$ units.