Point J is located at (2, 5) and point K is located at (4, 19) . What are the coordinates of the point that partitions the directed line segment JK⎯⎯⎯⎯⎯ in a 3:2 ratio? Enter your answer as decimals in the boxes.

The coordinates of the point that partitions the directed line segment JK in a 3:2 ratio is (3.2,13.4) and this can be determined by using the given data.

Given :

Point J is located at (2,5) and point K is located at (4,19).
Partitions the directed line segment JK in a 3:2 ratio.

The following steps can be used in order to determine the coordinates of the point that partitions the directed line segment JK in a 3:2 ratio:

Step 1 - The total number of partitions of the line JK is (3 + 2) 5.

Step 2 - The x-coordinate of the point is given by:

First, determine the horizontal distance that is:

4 - 2 = 2

Then divide the horizontal distance by 5.

[tex]=\dfrac{2}{5}[/tex]

Now, multiply the above expression by 3 and then add the x coordinate of point J.

[tex]=\dfrac{2}{5}\times 3 + 2[/tex]

= 3.2

Step 3 - The y-coordinate of the point is given by:

First, determine the vertical distance that is:

19 - 5 = 14

Then divide the vertical distance by 5.

[tex]=\dfrac{14}{5}[/tex]

Now, multiply the above expression by 3 and then add the y coordinate of point J.

[tex]=\dfrac{14}{5}\times 3 + 5[/tex]

= 13.4

So, the coordinates of the point that partitions the directed line segment JK in a 3:2 ratio is (3.2,13.4)

For more information, refer to the link given below:

https://brainly.com/question/2263981