The midpoint of line AB is M(2, 6).  If A has coordinates (10, 12). Then find the coordinates of point B.

We know, for two points (x₁, y₁) & (x₂, y₂):

 Midpoint $=\frac{{\mathrm{x}}_1+{\mathrm{x}}_2}{2},\frac{{\mathrm{y}}_1+{\mathrm{y}}_2}{2}$

Given, the mid-point = (2, 6)

And coordinates of A (x₁, y₁) = (10, 12) & let the coordinates of B = (x₂, y₂)

Then, on substitution:

$\Rightarrow (2,6)=\frac{10+{\text{x}}_2}{2},\frac{12+{\text{y}}_2}{2}$

$\Rightarrow \frac{10+{\text{x}}_2}{2}=2; \frac{12+{\text{y}}_2}{2}=6$

$\Rightarrow {\text{x}}_2=4-10; {\text{y}}_2=12-12$

$\Rightarrow {\text{x}}_2=-6, {\text{y}}_2=0$

 Thus, the coordinates of B = (- 6, 0).