Question

directed line segment DE has endpoints D(-4, -2) and E(1, 8). Point F divides DE such that DF:FE is 2:3. What are the coordinates of F?

Answer 1

Answer: (-2,2)

Step-by-step explanation:

The coordinates of the point P(x,y) which divides the line segment  joining M(a,b) and N (c,d) in ratio m:n is given by :-

$x=\dfrac{mc+na}{m+n},\ y=\dfrac{md+nb}{m+n}$

Given : Line segment DE has endpoints D(-4, -2) and E(1, 8).

Let (x,y) be the coordinates of point F which divides line segment DE in ratio 2:3.

Then , the coordinates of the point F(x,y) will be :-

$x=\dfrac{2(1)+3(-4)}{2+3},\ y=\dfrac{2(8)+3(-2)}{2+3}\\\\\Rightarrow\ x=-2,\ y=2$

Hence, the coordinates of F = (-2,2)

Answer 2

The answer is (-2,10)