Question

Find the coordinates of the points which trisect the line segment $AB$ where $A(2,1, -3)$ and $B(5, -8,3)$.

• A. $(4,-5,1)$, $(3,-2,-1)$
• B. $(-4,5,1)$, $(3, -2,-1)$
• C. $(-5,4,1)$, $(3,2,1)$
• D. $(4, 5, -1)$, $(3,2,1)$

Answer 1

Answer: (A)

$(4,-5,1)$, $(3,-2,-1)$

Answer 2

Let $C$ and $D$ be two points which trisect the join of $AB$. $\because C$ divides the join of $AB$ in the ratio $1 : 2$. $\therefore$ Coordinates of $C$ is $\left(\frac{1\times5+2\times 2}{1+2}, \frac{1\times \left(-8\right)+2\times 1}{1+2}, \frac{1\times 3+2\times \left(-3\right)}{1+2}\right)$ $= \left(3, -2,-1\right)$. Also, $D$ divides the join of $AB$ in the ratio $2 : 1$ $\therefore$ Coordinates of $D$ is $\left(\frac{2\times 5+1\times 2}{1+2}, \frac{2\times \left(-8\right)+1\times 1}{1+2}, \frac{2\times 3+1\times \left(-3\right)}{1+2}\right)$ $=\left(4, -5, 1\right)$