If $C$ is the mid-point of line segment $A B$ and $P$ is any point not on the line $A B$, then

Question

Aicharya · Accepted Answer

Here, $\mathbf{P C}$ is median and median of $\triangle P A B$.

$\begin{aligned} & \therefore & \mathbf{P C} & =\frac{\mathbf{P A}+\mathbf{P B}}{2} \\ & \Rightarrow & 2 \mathbf{P C} & =\mathbf{P A}+\mathbf{P B} \\ & \Rightarrow & \mathbf{P A}-\mathbf{P C} & =\mathbf{P C}-\mathbf{P B}\end{aligned}$

If $C$ is the mid-point of line segment $A B$ and $P$ is any point not on the line $A B$, then

Solution