Question 158662
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  = {{{2/3}}}* 6 = 4 units
Vertical side = {{{2/3}}}* 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
:
{{{7.2111/10.8167}}} = .6666 ~ {{{2/3}}}
:
Did this help?