Question

Point $C$ is the mid-point of line segment $AB$, prove that every line segment has one and only one mid-point.

Answer 1

$AC=BC$ ... $\left(i\right)$

If possible, let $D$ be another mid-point of $AB$.

$AD=DB$ ... $\left(ii\right)$

Subtracting $\left(ii\right)$ from $\left(i\right)$

$AC–AD=BC–DB$

$DC=-DC$ $(\because AC-AD=DCandCB-DB=-DC)$

$DC+DC=0$

$2DC=0$

$DC=0$

So, $C$ and $D$ coincide.

Thus, every line segment has one and only one mid-point.