Answer to Question #130884 in Analytic Geometry for Galata

Question

Find the distance between the following pair of points
A) the origin and (-√3,√6)

Answer 1

The distance , d , between two points (x_1,y₁) and (x₂,y₂) is given by d = $\sqrt{(x_1-x_2)^2 +(y_1-y_2)^2}$ So, here we have (x₁,y₁)=(0,0) and (x₂,y₂)=($-\sqrt3 ,\sqrt6$ )Hence distance is d = $\sqrt{\smash[b](0-(-\sqrt3))^2+(0-\sqrt6)^2}$ = $\sqrt{\smash[b](\sqrt3)^2+(\sqrt6)^2}$
=> d = $\sqrt{\smash[b]3+6} = \sqrt{\smash[b]9} = 3$ units.