Question

Find the points of trisection of the line segment joining $(4,1)$ and $(-2,-3)$.

Answer 1

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then

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

Let P and Q be the points of trisection of line joining the points A(4,1) & B(-2,-3).

Then, AP = PQ = QB

Now, P divides AB in the ratio 1:2 and Q divides AB in the ratio 2:1.

Therefore,

Coordinates of P = $(\frac{(-7+4)}{3},\frac{4-4}{3})=(-1,0)$

Coordinates of Q = $(\frac{(-14+2)}{3},\frac{8-2}{3})=(-4,2)$

Hence, the two points of trisection are $P(-1,0)$ and $(-4,2)$.