Question

$C$ is a point on the line segment joining the points $A(2,-3,4)$ and $B(8,0,10)$. If the value of $y$-coordinate of $C$ is $-2$, then the $z-$coordinate of $C$ is

• A. $4$
• B. $6$
• C. $-4$
• D. $5$

Answer 1

Answer: (B)

$6$

Let C divides line joining AB in ratio $a:b$

Let $C\equiv (x,y,z)\equiv (x,-2,\alpha )$

So, $-2=\frac{-3\left(b\right)+0\left(a\right)}{a+b}$

$-2a-2b=-3b$

So, $2a=b$

So, $z=\frac{4b+10a}{a+b}=\frac{4\left(2a\right)+10\left(a\right)}{a+2a}=\frac{18}{3}=6$