Find the coordinates of the point which divides the join A(3,2,5) and B(−4,2,−2) in the ratio 4:3 .

Engineering

Mathematics

Equation of Straight Line in 3D

Distance Formulae and Its Application

Section Formulae and Centres of a Triangle

Question

Find the coordinates of the point which divides the join A(3,2,5) and B(−4,2,−2) in the ratio 4:3 .

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Given:- A(3,2,5),B(-4,2,-2) & point C divide 4:3.

To Find:- Co-ordinate of point C.

Solution :

Let co-ordinate of point C be (x,y,z) that divides the line goining A & B in the ratio of 4:3 internally.

We know that Co-ordinate of C that divides the line seagment joining. A(x,y,z)&B(x₂,y₂,z₂ ) internally in the ratio m : n is

$c (x, y, z) = \frac{{mx}_{2} + {nx}_{1}}{m + n}, \frac{{my}_{2} + {ny}_{1}}{m + n}, \frac{{mz}_{2} + n_{2}}{m + n}$

putting the value of A & B in eq (i), we get

$= \frac{4 (- 4) + 3 (3)}{7}, \frac{4 \times 2 + 3 \times 2}{7}, \frac{4 (- 2) + 3 (5)}{7}$

$= \frac{- 16 + 9}{7}, \frac{8 + 6}{7}, \frac{- 8 + 15}{7}$

$= \frac{- 7}{7}, \frac{14}{7}, \frac{7}{7}$

Hence = –1,2,1.