Question

The coordinate of the points which trisect the line segment joining the points $A(2,1,-3)$ and $B(5,-8,3)$, are

• A. $(3,-2,-1)$ and $(4,-5,1)$
• B. $(3,2,1)$ and $(4,5,2)$
• C. $(-3,5,1)$ and $(3,4,-5)$
• D. None of the above

Answer 1

Answer: (A)

Let $R_1$ and $R_2$ are the points with coordinates $\left(x_1, y_1, z_1\right)$ and $\left(x_2, y_2, z_3\right)$ which trisect the line segment $A B$.

Now, $A R_1: R_1 B=1: 2$
$\Rightarrow x_1 =\frac{1 \times 5+2 \times 2}{1+2}=\frac{9}{3}=3$
$y_1 =\frac{1 \times(-8)+2 \times 1}{1+2}=\frac{-6}{3}=-2$
and $ z_1=\frac{1 \times 3+2 \times-3}{1+2}=\frac{-3}{3}=-1 $
$\therefore R_1=(3,-2,-1)$
Similarly, $A R_2: R_2 B=2: 1$
$\Rightarrow x_2=\frac{2 \times 5+1 \times 2}{1+2}=\frac{12}{3}=4$
and $ y_2=\frac{2 \times(-8)+1 \times 1}{1+2}=\frac{-15}{3}=-5 $
$z_2=\frac{2 \times 3+1 \times(-3)}{1+2}=\frac{3}{3}=1$
$\therefore$ Coordinates of $R_2$ are $(4,-5,1)$.