SOLUTION: Another problem that I don't know where to start: Given the points P1 (-4,-1) and P2 (8,3). Find the coordinates of the point R(x,y) on P1P2 (this has a line over it and the 1 a

Algebra ->  Length-and-distance -> SOLUTION: Another problem that I don't know where to start: Given the points P1 (-4,-1) and P2 (8,3). Find the coordinates of the point R(x,y) on P1P2 (this has a line over it and the 1 a      Log On


   

Question 1063647: Another problem that I don't know where to start:
Given the points P1 (-4,-1) and P2 (8,3). Find the coordinates of the point R(x,y) on P1P2 (this has a line over it and the 1 and 2 are subscript) so that the ratio P1R : RP2 = 3:1 (1 and 2 are subscript).
Found 2 solutions by Fombitz, KMST:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the x distance from P%5B1%5D to P%5B2%5D.
x=8-%28-4%29=12
Divide this up into 4 equal sections.
dx=12%2F4=3
So then the x distance from P%5B1%5D to R%5D%7D%7D+is+3+of+these+equal+sections%2C%0D%0AStarting+at+%7B%7B%7BP%5B1%5D,
x%5BR%5D=-4%2B3%283%29=-4%2B9=5
Similarly for the y distance,
Find the y distance from P%5B1%5D to P%5B2%5D.
y=3-%28-1%29=4
Divide this up into 4 equal sections.
dy=4%2F4=1
So then the y distance from P%5B1%5D to R%5D%7D%7D+is+3+of+these+equal+sections%2C%0D%0AStarting+at+%7B%7B%7BP%5B1%5D,
y%5BR%5D=-1%2B3%281%29=-1%2B3=2
So the coordinates of R are (5,2).

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The line over P%5B1%5DP%5B2%5D means
that they are talking about the line segment
joining those two points.

You are looking for the coordinates of a point R ,
on that line segment that meets the requirement that
P%5B2%5DR%2FRP%5B2%5D=3%2F1 .
In other words,
the distance from R to P%5B1%5D is 3 times
the distance from R to P%5B2%5D .
Dividing the original segment into
3%2B1=4 equal pieces, R is
the"dividing point" closest to P%5B2%5D .
In this case, if M is the midpoint of segment P1P2,
R is the midpoint of segment MP2.