In triangleABC
D is a point on BA such that BDA = 1:2
E is a point on CB such that CE:EB = 1:4
DC and AE intersect at F
I am suppose to find CF:FD(express the ratio in terms of two positive whole numbers) Help!
Hello kgkYou can solve this using ratios and position vectors. See my post at http://www.mathhelpforum.com/math-he...tml#post262231 for the basic formula.
In your problem, if we denote the position vectors of A, B, ... by then
If we suppose that F divides CD in the ratio 1:n, and EA in the ratio 1:m, then have two ways of expressing .
Using CF:CD = 1:n,
Using EF:FA = 1:m,
If we equate these two expressions for and compare coefficients of , and , we get:
(1)
(2)
(3)
From (2) and (3):
Check: . Subst into (1):
So the ratio CF:FD = = 3:8.
Grandad