The midpoint of the line segment AB has coordinates of (1, - 2) if  A's coordinates are (-3, 2) then find the coordinate of point B.

Given that, the coordinates of the midpoint of line segment AB are (1, - 2).

 Also, the coordinates of A are (- 3, 2).

Let the coordinates of B be (a, b)

The midpoint of two points $\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)$and $\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)$ is calculated by the formula $\left(\frac{{\mathrm{x}}_1+{\mathrm{x}}_2}{2},\frac{{\mathrm{y}}_1+{\mathrm{y}}_2}{2}\right)$

Hence, the midpoint of $\mathrm{AB}=\left(\frac{-3+\mathrm{a}}{2},\frac{2+\mathrm{b}}{2}\right)=(1,-2)$

$\Rightarrow \frac{-3+\mathrm{a}}{2}=1; \frac{2+\mathrm{b}}{2}=-2$

$=-3+\mathrm{a}=2 , 2+\mathrm{b}=-4$

$\therefore \mathrm{a}=5, \mathrm{b}=-6$

Hence, the coordinates of B are (5, - 6).