Question

If $A(-2,5),B(3,1)$ are two points and $P,Q$ are the points of trisection of $\overline{AB}$, then mid point of $\overline{PQ}$ is:

Answer 1

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

If P and Q are the points trisection of $A(-2,5)$ and $B(3,1)$

then mid-point of PQ coincides with mid-point of AB

So, m = 1 and n = 1

$\therefore$ Mid-point PQ

$=(\frac{-2+3}{2},\frac{5+1}{2})=(\frac{1}{2},3)$