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

$\frac{mx_2+nx_1}{m+n}_{},\frac{my_2+ny_1}{m+n}$

In this case,

$m=3,n=2$

Therefore,

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

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