The distance between two points $$A$$ and $$B$$ on the plane is the module of the fixed vector that determines: $$$d(A,B)=|\overrightarrow{AB}|$$$ In coordinates, if $$A=(a_1,a_2)$$ and $$B =(b_1,b_2)$$, then we have: $$$d(A,B)=|\overrightarrow{AB}|=|(b_1-a_1,b_2-a_2)|=\displaystyle \sqrt{(b_1-a_1)^2+(b_2-a_2)^2}$$$
To calculate the distance between points $$A = (3, 4)$$ and $$B = (2,-5)$$. $$$d (A, B) =|\overrightarrow{AB}| = | (2-3,-5-4) | = | (-1,-9) | = \displaystyle \sqrt{(-1)^2+(-9)^2}=\sqrt{82}$$$