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=

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.