Question

The distance between the points (m, -n) and (-m, n) is

Answer 1

$$\textbf{Step -1: Applying Distance formula to find distance between two given points}$$

$$\text{The distance between two points }(x_1,y_1)\text{ and }(x_2,y_2)\text{ is given by,}$$

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

$$\text{Here, the given points are }(m,-n)\text{ and }(-m,n)$$

$$\therefore d=\sqrt{((-m)-m)^2+(n-(-n))^2}$$

$$=\sqrt{(-2m)^2+(2n)^2}$$

$$=\sqrt{4m^2+4n^2}$$

$$=2\sqrt{m^2+n^2}$$

$$\textbf{Hence, The distance between the points }\mathbf{(m,-n)}\textbf{ and }\mathbf{(-m,n)}\textbf{ is }\mathbf{2\sqrt{m^2+n^2}}$$