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 $(x, y, z)=\left(\frac{20}{7}, \frac{5}{7}, \frac{15}{7}\right)$