SOLUTION: The Question is: Consider the line segment determined by A(-1,2) and B(5,11). Find the coordinates of a point P such that AP/PB=2/1. I have no idea where to start with this pro

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Question 158662This question is from textbook College Algebra
: The Question is:
Consider the line segment determined by A(-1,2) and B(5,11). Find the coordinates of a point P such that AP/PB=2/1.
I have no idea where to start with this problem... My solution manual states that the point "must" lie 2/3 of the distance from A to B.
My question is... How does someone find out that the point "must" be 2/3 the distance from A to B.
I understand from the problem that line segment AP is twice as long as line segment PB. I found a midpoint (2,13/2) and the quarter point (7/2,35/4)and thought somehow I could come up with the 2/3 that they start with in the manual.
Please explain how you get to the 2/3 distance.
Thanks to all you tutors out there! This question is from textbook College Algebra

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Consider the line segment determined by A(-1,2) and B(5,11). Find the coordinates of a point P such that AP/PB=2/1.
I have no idea where to start with this problem... My solution manual states that the point "must" lie 2/3 of the distance from A to B.
:
Think of the segment as being the hypotenuse of a right triangle.
Plotting this segment on graph paper will illustrate this.
:
Note that:
the horizontal side is 5 -(-1) = 6 units
the vertical side is 11 - 2 = 9 units
:
Find the 2/3 segment:
Horizontal side = * 6 = 4 units
Vertical side = * 9 = 6 units
:
Find the xy coordinates of 2/3 the segment:
x: 4 - 1 = 3
y: 6 + 2 = 8
:
xy Coordinates of 2/3 segment: 3, 8
:
You can prove this, find the hypotenuse of the original line
h = Sqrt(6^2 + 9^2) = 10.8167
The hypotenuse of the 2/3 segment
h = Sqrt(4^2 + 6^2) = 7.2111
:
= .6666 ~
:
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