Question

A point R with x – coordinates 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.​

Answer 1

Answer:

points are P (x1, y1, z 1) and Q (x2, y2,z2)

Let R divide the line in ratio k:1

Then coordinates of point R are:

(k×8 + 1×2)/(k+1), (k×0 + 1×(-3))(k+1), (k×10 + 1×4)/(k+1)

(8k+2)/(k+1), 3/(k+1), (10k + 4)/(k+1)

(8k + 2)/(k+1) = 4

8k + 2= 4k +4

k = 1/2

put this value of k in other two coordinates, you will get

y = - 2 and z = 6

So coordinates of R are 4, -2 , 6