Question

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

Answer 1

Let P (x₁, y₁) and Q (x₂, y₂) be the points of trisection of the line segment joining the given points i.e., AP = PQ = QB

Therefore, point P divides AB internally in the ratio 1:2.
$x_1=\frac{1\times(-2)+2\times4}{1+2}$, $y_1=\frac{1\times (-3)+2\times(-1)}{1+2}$
$x_1=\frac{-2+8}{3}=\frac{6}{3}=2$, $y_1=\frac{-3-2}{3}=\frac{-5}{3}$

Point Q divides AB internally in the ratio of 2:1.
$x_2=\frac{2\times(-2)+1\times4}{2+1}$ , $y_2=\frac{2\times(-3)+1\times(-1)}{2+1}$
$x_2=\frac{-4+4}{3}=0$ , $y_2=\frac{-6-1}{3}=\frac{-7}{3}$

Q (x₂, y₂) = $(0,-\frac{7}{3})$