Question

find the coordinates of the point which divides externally the line segment joining (1,- 3) and (-3,9) in the ratio 1:3

Answer 1

let the point be P(x,y)
x=(m2x1+m1x2)÷(m1+m2).
=>(3×1+1×-3)÷(1+3)
=>(3-3)÷4
=>0/4
=>0

y=(y2m1+y1m2)÷(m1+m2)
=>(9×1+3×-3)÷(1+3)
=>(9-9)÷4
=>0\4
=>0
so, P(0,0)
It's origin.
I hope this answer helps you.

Answer 2

coordinates of the point (1,- 3) and (-3,9)

ratio 1:3

m=1  .n=3

x1=1 , x2= -3  ,y1 =3 , y 2=9

The formula for the co-ordinates of a point which divides a line externally by m:n is given by

P=([mx2 - nx1]/[m - n])  ,([my2 - ny1]/[m - n])

P=([1 *-3 - 3*1]/[1 - 3]) ,  ([1* 9 - 3*3]/[1 - 3])

P=([-3-3]/[-2])  ,  ([ 9-3]/[-2])

P=[-6\-2],   [6/-2]

P=(3  ,-3 )