Question

The coordinates of the point P which divides the line segment joining A(1,-2,3) and B(3,4,-5) internally in the ratio 2:3 is

• A. (9,2,-1)
• B. $P=(\frac{9}{5},\frac{2}{5},\frac{-1}{5})$
• C. (-3,-14,19)
• D. $P=(\frac{3}{5},\frac{14}{5},\frac{-19}{5})$

Answer 1

The correct option is B

$P=(\frac{9}{5},\frac{2}{5},\frac{-1}{5})$

Let P(x,y,z) divide the line segment joining A(1,-2,3) and B(3,4,-5) internally in the ratio 2:3. Therefore,

$x=\frac{2\times 3+3\times 1}{2+3}=\frac{9}{5}y=\frac{2\times 4+3\times (-2)}{2+3}=\frac{2}{5}z=\frac{2\times (-5)+3\times 3}{2+3}=\frac{-1}{5}$

$P=(\frac{9}{5},\frac{2}{5},\frac{-1}{5})$