SOLUTION: A line passes through A(1,1) and B(4,3). Find the coordinates of the point on the line which is 3 times as far from A s from B.

Algebra ->  Length-and-distance -> SOLUTION: A line passes through A(1,1) and B(4,3). Find the coordinates of the point on the line which is 3 times as far from A s from B.      Log On


   

Question 964639: A line passes through A(1,1) and B(4,3). Find the coordinates of the point on the line which is 3 times as far from A s from B.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
In the x-direction, the distance from A to B is 4-1=3.
If the distance from A to point P is equal to 3x, the distance from P to B is equal to x.
Then the distance from A to B would be 3x%2Bx=4x
4x=3
x=3%2F4
So then starting at A,
P%5Bx%5D=1%2B3%283%2F4%29
P%5Bx%5D=1%2B9%2F4
P%5Bx%5D=13%2F4
Similarly for y, the y distance is 3-1=2
4y=2
y=1%2F2
Again starting at A,
P%5By%5D=1%2B3%281%2F2%29
P%5By%5D=1%2B3%2F2
P%5By%5D=5%2F2
(13%2F4,5%2F2)