Question

What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4?

Answer 1

Explanation:

The complete question is shown in the attached file. We know that:

$J(x_{1},y_{1})=J(-15,-5) \\ \\ K(x_{2},y_{2})=K(25,15) \\ \\ \\ m:n=1:4 \\ \\ \\ So: \\ \\ m=1 \\ \\ n=4$

From the formulas:

$x=\left(\frac{m}{m+n}\right)(x_{2}-x_{1})+x_{1} \\ \\ \\ Substituting \ values: \\ \\ x=\left(\frac{1}{1+4}\right)(25-(-15))-15 \\ \\ x=\left(\frac{1}{5}\right)(40)-15 \\ \\ x=8-15 \\ \\ x=-7$

$y=\left(\frac{m}{m+n}\right)(y_{2}-y_{1})+y_{1} \\ \\ \\ Substituting \ values: \\ \\ y=\left(\frac{1}{1+4}\right)(15-(-5))-5 \\ \\ y=\left(\frac{1}{5}\right)(20)-5 \\ \\ y=4-5 \\ \\ y=-1$

Finally:

$\boxed{E(-7,-1)}$