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)

I added a screenshot of the complete question.

(-7, -1)

Explanation:

The formulas given to calculated the x and y coordinates are as follows:

Let's define the variables used:

(x₁ , y₁) are the coordinates of the first point while (x₂ , y₂) are the coordinates of the second point.

We are given that the segment is directed from J to K, therefore:

First point is J ..........> (x₁ , y₁) is (-15, -5)

Second point is K ....> (x₂ , y₂) is (25, 15)

m and n defined the portion of the partitioned segment (JE : EK). It is given that this ratio is 1:4. Therefore:

m = 1 and n = 4

Finally, let's substitute with these variables in the equations as follows:

Based on the above, the coordinates of point E are (-7, -1)

Hope this helps :)

(-7,-1)

Step-by-step explanation:

Given that the point J has coordinates as (-15,-5) and K has coordinates as

(25,15)

E divides the line segment JK in the ratio 1:4 internally

Here the ratio is m:n where m =1 and n =4

The formula for a point dividing the line joining (x1,y1) and (x2,y2) in the ratio m:n is

Substitute for m,n and also other points

WE get

Coordinate of E=

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!