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Question 1008389: find the coordinates of the point which divides the line segment from (-1,4) to (2,-3) in to ratio of 3 to 4 (two solutions)
Found 3 solutions by mananth, ikleyn, n2:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! Let the points be (x1,y1) and (x2,y2)
Here
x1= -1
x2= 2
y1= 4
= -3
ratio of division
m= 3
n= 4
The the coordinates the point which divides the two points in the ration of m:n is given by
x= 
Y 
plug thevalues
x=( 3 * 2 + 4 * 2 )( 3 + 4 )
x=( 6 + 8 )( 7 )
x=( 14 / 7
x= 2
y=( 3 * -3 + 4 * 4 )( 3 + 4 )
y=( -9 + 16 )( 7 )
y=( 7 / 7
y=( 1
The co ordinates are x= 2 ,y= 1
Now plug m=4 and n=3 to get other solution
m.ananth@hotmail.ca
Answer by ikleyn(53742)  (Show Source):
You can put this solution on YOUR website! .
find the coordinates of the point which divides the line segment from (-1,4) to (2,-3) in to ratio of 3 to 4
(two solutions)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Calculations and the answer in the post by @mananth are totally and fatally incorrect.
His formulas are conceptually and methodically incorrect;
his calculations are partly incorrect and partly incomplete.
Below is my correct solution.
The points are A = (x1,y1) = (-1,4) and B = (x2,y2) = (2,-3).
Ratio of division is m:n = 3:4.
If to interpret the ratio 3:4 as starting from A to B,
then the coordinates of the point which divides the given segment are
x =  =  =  ,
y =  =  =  = 1,
If to interpret the ratio 3:4 as starting from B to A,
then the coordinates of the point which divides the given segment are
x =  =  =  ,
y =  =  =  .
ANSWER. If to count the ratio 3:4 from A to B, then the division point is (, ).
If to count the ratio 3:4 from B to A, then the division point is (,).
Solved correctly.
Answer by n2(78)  (Show Source):
You can put this solution on YOUR website! .
find the coordinates of the point which divides the line segment from (-1,4) to (2,-3) in to ratio of 3 to 4
(two solutions)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The points are A = (x1,y1) = (-1,4) and B = (x2,y2) = (2,-3).
Ratio of division is m:n = 3:4.
If to interpret the ratio 3:4 as starting from A to B,
then the coordinates of the point which divides the given segment are
x = = = ,
y = = = = 1,
If to interpret the ratio 3:4 as starting from B to A,
then the coordinates of the point which divides the given segment are
x = = = ,
y = = = .
ANSWER. If to count the ratio 3:4 from A to B, then the division point is (,).
If to count the ratio 3:4 from B to A, then the division point is (,).
Solved.
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