Question

Find the coordinates of the point which is three fifth of the way from $(3,4,5)$ to $(-2,-1,0)$.

• A. $(1,0,2)$
• B. $(2,0,1)$
• C. $(0,2,1)$
• D. $(0,1,2)$

Answer 1

Answer: (D)

Let $A=(3,4,5)$, $B=(-2,-1,0)$ and $P(x,y,z)$ be the required point. As $P$ is three-fifth of the way from $A$ to $B$. So, $P$ divides $[AB]$ in the ratio $3:2$.
$\therefore P\equiv \left(\frac{3\times \left(-2\right)+2\times 3}{3+2},\frac{3\times \left(-1\right)+2\times 4}{3+2},\frac{3\times 0+2\times 5}{3+2}\right)$,
$\Rightarrow P=\left(0,1,2\right)$.