Question

Find the co-ordinates of the point which divides the line segment joining the points A (4, -2, 5) and B (-2, 3.7) externally in the ratio 8 :5.

Answer 1

Answer:

Co-ordinates of point are (-12,34/3,31/3)

Step-by-step explanation:

To find the co-ordinates of the point which divides the line segment joining the points A (4, -2, 5) and B (-2, 3.7) externally in the ratio 8 :5.we must use section formula for external division

A(x1,y1,z1)

B(x2,y2,z2)

let the point P(x,y,z) divides the line segments of joining AB in m:n ratio externally,so,coordinates of P

$x=\frac{mx_{2}-nx_{1}}{m-n}\\ \\ \\y=\frac{my_{2}-ny_{1}}{m-n}\\ \\ \\z=\frac{mz_{2}-nz_{1}}{m-n}$

so put this formula for the given points and given ratio

$x=\frac{8(-2)-5(4)}{8-5}\\\\\\x=\frac{-16-20}{3}\\\\\\x=-12\\\\y=\frac{24+10}{8-5}\\ \\y=\frac{34}{3}\\\\\\z=\frac{56-25}{3}\\\\\\z=\frac{31}{3}$

so,co-ordinates of point are (-12,34/3,31/3)