Question

The co-ordinates of the point of trisection of the line segment joining the points $(-4,3)$ and $(2,-1)$ are

• A. $(2,1)$
• B. $(3,1)$
• C. $(-2,\frac{5}{3})$
• D. None of these

Answer 1

Answer: (C)

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

The points are $P=(x_1,y_1)=(-4,3)$ and $Q=(x_2,y_2)=(2,-1)$.

The segment $PQ$ is trisected at $R=(X,Y)$ in the ratio $m:n$.

Then $m:n=1:2$ & $m+n=3$.

$\therefore X=\frac{m{x}_2+n{x}_1}{m+n}=\frac{1\times 2+2\times (-4)}{3}=-2$

And $Y=\frac{m{y}_2+n{y}_1}{m+n}=\frac{1\times (-1)+2\times 3}{3}=\frac{5}{3}$

$\therefore (X,Y)=(-2,\frac{5}{3})$

Then $m:n=2:1$ & $m+n=3$.

$\therefore X=\frac{m{x}_2+n{x}_1}{m+n}=\frac{2\times 2+1\times (-4)}{3}=0$

And $Y=\frac{m{y}_2+n{y}_1}{m+n}=\frac{2\times (-1)+1\times 3}{3}=\frac{5}{3}$

$\therefore (X,Y)=(0,\frac{5}{3})$ also.