Problem involving points on a line.

Question

Given two points A(-3,4) and B(2,5) find the coordinates of one point P on the line and passing por A and B. Look that the point P is two times more distant from A than B.

Answer 1

1) Find the equation of the line connecting the two points. P must fulfill this equation since it is on the line.

2) Let's assume that d(x,y) is the distance between x and y, then your second constraint "the distance of P from A is twice the distance from P to B" can be written as: d(A,P)=2*d(B,P). You should know how to calculate d(x,y), so just insert into both sides of the equation.

3) Using the equations from (1) and (2), you have two equations with two variables, solve this simple system of equations and you will find P.

Good luck!

Answer 2

Hint: Since your point P lies on $AB$, this just finding an inner point formula: $$AP:PB=2:1$$