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

Step-by-step 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((m)/(m+n)\right)(x_(2)-x_(1))+x_(1) \\ \\ \\ Substituting \ values: \\ \\ x=\left((1)/(1+4)\right)(25-(-15))-15 \\ \\ x=\left((1)/(5)\right)(40)-15 \\ \\ x=8-15 \\ \\ x=-7`

`y=\left((m)/(m+n)\right)(y_(2)-y_(1))+y_(1) \\ \\ \\ Substituting \ values: \\ \\ y=\left((1)/(1+4)\right)(15-(-5))-5 \\ \\ y=\left((1)/(5)\right)(20)-5 \\ \\ y=4-5 \\ \\ y=-1`

Finally:

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