Question

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

Answer 1

The Solution.

The given points are

`D(-4,-2)\text{ and E(1,8)}`

The formula is

`(mx_2+nx_1)/(m+n)_{},(my_2+ny_1)/(m+n)`

In this case,

`m=3,n=2`

Therefore,

`\begin{gathered} ((mx_2+nx_1)/(m+n)_{},(my_2+ny_1)/(m+n)) \\ =(\frac{3(1)+_{}2(-4)_{}}{3+2}_{},\frac{3(8)_{}+2(-2)_{}}{3+2}) \\ \end{gathered}`
`=((3-8)/(5),(24-4)/(5))=(-(5)/(5),(20)/(5))`
`=(-1,4)`

Hence, the correct answer is (-1, 4) (option 3)