A point R with x-coordinate 4 lies on the line segment joining the points P(2,−3,4) and Q(8,0,10). Find the coordinates of the point R.
The coordinates of points P and Q are given as P(2,−3,4) and (8,0,10)
Let R divide line segment PQ in the ratio k:1
Hence by section formula, the coordinates of point R are given by,
(k(8)+2k+1,k(0)−3k+1,k(10)+4k+1)=(8k+2k+1,−3k+1,10k+4k+1)
It is given that the x-coordinate of point R is 4.
∴8k+2k+1=4
⇒8k+2=4k+4
⇒4k=2
⇒k=12
Therefore, the coordinates of point R are ⎛⎜
⎜⎝4,−312+1,10(12)+412+1⎞⎟
⎟⎠=(4,−2,6)