SOLUTION: Find the point dividing the interval AB in the ratio 1:3 if A(-1,1) and B is (3,-1)

Algebra ->  Linear-equations -> SOLUTION: Find the point dividing the interval AB in the ratio 1:3 if A(-1,1) and B is (3,-1)      Log On


   



Question 1115405: Find the point dividing the interval AB in the ratio 1:3 if A(-1,1) and B is (3,-1)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Find the point dividing the interval AB in the ratio 1%3A3 if A(-1,1) and B is (3,-1)
To find the point P that divides a segment AB into a particular ratio, determine the ratio k by writing the numerator over the sum of the numerator and the denominator of the given ratio.
Next, find the rise and the run (slope) of the line. Finally, add k times the run to the x-coordinate of A and add k times the rise to the y-coordinate of A.
This process is summarized with the following formula:

P(x,y)=(x%5B1%5D%2Bk%28x%5B2%5D-x%5B1%5D%29 , y%5B1%5D%2Bk%28y%5B2%5D-y%5B1%5D%29 )
you have:
k=1%2F3
A(-1,1) => x%5B1%5D=-1, y%5B1%5D=1
and
B is (3,-1) => x%5B2%5D=+3, y%5B2%5D=-1

(x,y)=(-1%2B%281%2F3%29%283-%28-1%29%29 , 1%2B%281%2F3%29%28-1-1%29 )
(x,y)=(-1%2B%281%2F3%29%283%2B1%29 , 1%2B%281%2F3%29%28-2%29 )
(x,y)=(-1%2B4%2F3 , 1-2%2F3 )
(x,y)=(-3%2F3%2B4%2F3 , 3%2F3-2%2F3 )
(x,y)=(1%2F3 ,+1%2F3 )