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? (–13, –3) (–7, –1) (–5, 0) (17, 11)

Answer 1

Answer: (-7,-1)

Complete question is attached below

The coordinates of J is (-15,-5) and K is (25,15)

The formula to find point E (x,y) is

$x=\frac{m}{m+n}(x_2-x_1)+x_1$

$y=\frac{m}{m+n}(y_2-y_1)+y_1$

We know the ratio is 1:4

m=1  and n=4

(x1,y1) is (-15,-5) and (x2,y2) is (25,15)

Now plug in all the values in the formula and find out x and y

$x=\frac{1}{1+4}(25-(-15))-15=\frac{1}{5}*40 - 15 = -7$

$y=\frac{1}{1+4}(15-(-5))-5=\frac{1}{5}*20 -5=-1$

The point E is (-7,-1)