Short Answer P(6/5,y) = P(1.2,y)
Remark
This problem is solved by a formula known as the section formula. If you want to divide a line into any ratio other than 1:1, this formula will do it for you.
Givens
Line segment with endpoints (-4,-8) and (9,3)
y2 = 3
y1 = -8
x2 = 9
x1 = - 4
m=2
n = 3
Desired ratio
m = 3
n = 2
m:n = 3:2
Formula
P(x,y) = [tex] P(\frac{m*x2 + n*x1}{m+n}, \frac{m*y2 +n*y1}{m+n} ) [/tex]
Sub and Solve
P(x,y) = [tex] \frac{2*9 + 3*(-4}{2 + 3}, \frac{2*3 + 3*(-8)}{2 + 3}
[/tex]
P(x,y) = [tex] \frac{18 - 12 }{5} , \frac{6 - 24}{5} [/tex]
P(x,y) [tex] \frac{6}{5} , \frac{-18}{5} [/tex]
conclusion
The point you want is
P(6/5,-18/5) If you measure the length with a ruler, you should see that the ratio the line is cut into is 2 : 3
Note: This question all depends on where you start from and what you call (x1,y1) and (x2,y2). Be prepared to argue the point if this answer is incorrect. Point C on my graph is the answer.
