Question

The co-ordinates of the point which divides the join of the points $(2,-1,3)$ and $(4,3,1)$ in the ratio $3:4$ internally are given by:

• A. $\frac{2}{7},\frac{20}{7},\frac{10}{7}$
• B. $\frac{10}{7},\frac{15}{7},\frac{2}{7}$
• C. $\frac{20}{7},\frac{5}{7},\frac{15}{7}$
• D. $\frac{15}{7},\frac{20}{7},\frac{3}{7}$

Answer 1

Answer: (C)

Given points are $(2,-1,3)$ and $(4,3,1)$ and ratio is $3:4$
$\Rightarrow x_1=2,y_1=-1,z_1=3,x_2=4,y_2=3,z_2=1$
and $m=3,n=4$
$\therefore$ By above formula, we have
$x=\frac{m{x}_2+n{x}_1}{m+n}=\frac{3\times 4+4\times 2}{3+4}=\frac{12+8}{7}=\frac{20}{7}$
$y=\frac{m{y}_2+n{y}_1}{m+n}=\frac{3\times 3+4\times -1}{3+4}=\frac{9-4}{7}=\frac{5}{7}$
$z=\frac{m{z}_2+n{z}_1}{m+n}=\frac{3\times 1+4\times 3}{3+4}=\frac{3+12}{7}=\frac{15}{7}$
$\therefore$ Co-ordinates $(x,y,z)=\left(\frac{20}{7},\frac{5}{7},\frac{15}{7}\right)$