Question

Find the ratio in which -3,p divide the line segment joining the point (-5,-4) (-2,3) find the point p

Answer 1

let the ratio be m:n.

use section formula.

(x,y)=(mx2 +mx1/m+n , my2+my1/m+n).

( -3 ,p)= -2m-5n/m+n

-2m-5n/m+n =3

cross multiply

-2m-5n=3m+3n

-2m-3m=3n+5n

-5m=8n

m/n=8/-5

m:n=8:-5

then find p

Answer 2

Answer:

let the point [-3,p] divide the line in the ration m:n

let [-5,-4] be [x1,y1] and [-2,3] be [x2,y2]

using section formula for x,

x=[mx2 +nx1]÷m + n

-3 = [-2m -5n]÷m +n

-3m -3n = -2m - 5n

2n = m

m:n = 2:1-------------.ratio

applying section formula for y,

y=[my2 +ny1]÷m + n

p = [3m - 4n]÷m+ n

p =[3*2 - 4] ÷ 1+2

   =2/3