Question

Find the value of $a$, for which point $P(a,2)$ is the midpoint of the lines segment joining the points $Q(-5,4)$ and $R(-1,0)$ .

Answer 1

If $(x_1,y_1)$ and $(x_2,y_2)$ are the coordinates of two points, then the coordinates of the mid point of the line joining these points is given by:

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

So, if the mid point of $(-5,4)$ and $(-1,0)$ is $(9,2)$, then using the mid-point formula:

$(\frac{-5-1}{2},\frac{4+0}{2})=(a,2)$

$(-3,2)=(a,2)$

On comparing the co-ordinates:

$a=-3$.