Find the coordinate of the points which trisect the line segment joining the points A $(2,1,-3)$ and $\mathrm{B}$ $(5,-8,3)$

Home » Find the coordinate of the points which trisect the line segment joining the points A and

Find the coordinate of the points which trisect the line segment joining the points A $(2,1,-3)$ and $\mathrm{B}$ $(5,-8,3)$

CBSE | Class 11 | Introduction to Three Dimensional Geometry | Maths | NCERT Exemplar

Find the coordinate of the points which trisect the line segment joining the points A $(2,1,-3)$ and $\mathrm{B}$ $(5,-8,3)$

Solution:

It is given the line segment joining the points are A $(2,1,-3)$ and $B(5,-8,3)$ Now suppose $P\left(x_{1}, y_{1}, z_{1}\right)$ and $Q\left(x_{2}, y_{2}, z_{2}\right)$ be the points which trisects the line segment.
$\Rightarrow$ P divides $A B$ in the ratio $2: 1$
$\Rightarrow \mathrm{x}_{1}=\frac{2+2 \times 5}{1+2}=4$
$\Rightarrow \mathrm{y}_{1}=\frac{1+2 \times(-8)}{1+2}=-5$
$\Rightarrow \mathrm{z}_{1}=\frac{-3+2 \times 3}{1+2}=1$
$\Rightarrow \mathrm{Q}$ divides $\mathrm{AP}$ in the ratio $1: 1$ $\Rightarrow \mathrm{x}_{2}=\frac{2+4}{2}=3$
$\begin{array}{l} \Rightarrow \mathrm{x}_{2}=\frac{2+4}{2}=3 \\ \Rightarrow \mathrm{y}_{2}=\frac{1+(-5)}{2}=-2 \\ \Rightarrow \mathrm{z}_{2}=\frac{-3+1}{2}=-1 \end{array}$
$\therefore(4,-5,1)$ and $(3,-2,-1)$ are the coordinate of the points which trisect the line segment joining the points A $(2,1,-3)$ and $B(5,-8,3)$ .