Question

Find the ratio in which the line segment joining the points $(4, 8,10)$ and $(6, 10, -8)$ is divided by the $yz$-plane.

• A. $2:3$ internally
• B. $2:3$ externally
• C. $5 :7$ internally
• D. $5:7$ externally

Answer 1

Answer: (B)

$2:3$ externally

Answer 2

Let $yz$-plane divides the line segment joining $A(4, 8, 10)$ and $B(6, 10, - 8 )$ at $P(x, y, z)$ in the ratio $k : 1$. Then the coordinates of $P$ are $\left(\frac{4+6k}{k+1}, \frac{8+10k}{k+1}, \frac{10-8k}{k+1}\right)$ Since $P$ lies on the $yz$- plane, its $x$-coordinate is zero, i.e., $\frac{4+6k}{k+1} = 0$ $\Rightarrow k = -\frac{2}{3}$ Therefore, $yz$-plane divides $AB$ externally in the ratio $2:3$.