Question

P(-1,2 ) is a point on the line segment A (3,6) and B (x,y) such that AP:PB 2:3

Answer 1

A=(x1,y1)=(3,6)
B=(x2,y2)=(x,y)
p=(x3,y3)=(-1,2)
AP:PB=m:n=2:3



x3=mx2+nx1/m+n
-1=(2*x+3*3)/2+3
-1=(2x+9)/5
-1*5=2x+9
-5=2x+9
-5-9=2x
x=-14/2=-7

y3=(my2+ny1)/m+n
2=(2*y+3*6)/2+3
2*5=2y+18
2y=10-18
=-8
y=-8/2=-4


B(-7,-4)