# If P (2, p) is the mid-point of the line segment joining the points

Question:

If P (2, p) is the mid-point of the line segment joining the points A (6, −5) and B (−2, 11). find the value of p.

Solution:

It is given that mid-point of line segment joining $A(6,-5)$ and $B(-2,11)$ is $P(2, p)$

In general to find the mid-point $\mathrm{P}(x, y)$ of two points $\mathrm{A}\left(x_{1}, y_{1}\right)$ and $\mathrm{B}\left(x_{2}, y_{2}\right)$ we use section formula as,

$\mathrm{P}(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

So,

$(2, p)=\left(\frac{6-2}{2}, \frac{-5+11}{2}\right)$

Now equate the y component to get,

$p=3$