Question

A point C with z-coordinate 8 lies on the line segment joining the points A(2, -3, 4) and B(8, 0, 10). Find the co-ordinates.

Answer 1

Let the co-ordinates of C be (x, y, 8) that divides in the ratio m : n

∴ \(\frac{m.10+n.4}{m+n}=8\)

⇒ 10m + 4n = 8m+ 8n 

⇒ 2m= 4n 

⇒ m= 2n

⇒ m: n = 2: 1

\(x=\frac{2.8+1.2}{2+1}=\frac{18}{3}=6\)

And

\(y=\frac{2.0+1.(-3)}{2+1}=-1\)

∴ Co-ordinate of C are (6, −1, 8).