First slide

Introduction to 3-D Geometry

Question

If the z-coordinate of a point on the line joining the points $B (3, - 2, 2)$ and $C (6, - 17, - 4)$ is $0$ , Then x-coordinate of the point is

Easy

A

2
B

$- 2$
C

3
D

4

Solution

Suppose that a point $P$ divides the line segment joining the points $B (3, - 2, 2)$ and $C (6, - 17, - 4)$ in the ratio $m : n$
Since the z coordinate is given zero, it implies that $\frac{2 m - 4 n}{m + n} = 0$
It gives
$\begin{matrix} 2 m - 4 n = 0 \\ 2 m = 4 n \\ \frac{m}{n} = \frac{2}{1} \end{matrix}$
The $x -$ coordinate of the point $P$ is $\frac{2 (3) + 1 (6)}{2 + 1} = \frac{12}{3} = 4$

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