Question

What is the x-coordinate of the point that divides EF into a 2:3 ratio?

3.8

–3.6

1.2

1.4

Answer 1

(x-(-4))/(9-x)=2/3
(x+4)/(9-x)=2/3
3(x+4)=2(9-x)
3x+12=18-2x
5x=6
x=6/5 = 1.2

Answer 1.2

Answer 2

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) =
`P((m*x2 + n*x1)/(m+n), (m*y2 +n*y1)/(m+n) )`

Sub and Solve
P(x,y) =
`(2*9 + 3*(-4)/(2 + 3), (2*3 + 3*(-8))/(2 + 3)`
P(x,y) =
`(18 - 12 )/(5) , (6 - 24)/(5)`
P(x,y)
`(6)/(5) , (-18)/(5)`

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.