Point j is located at (2,5)(2,5) and point k is located at (4,19)(4,19).

what are the coordinates of the point that partitions the directed line segment jk in a 3: 23: 2 ratio?

We have the coordinates
J (2,5)
K (4,19)

Since we are to find the point that partitions the line segment into 3:2 ratio, we have 5 equal parts of the line segment. So,

Get the horizontal distance:
4 - 2 = 2
Divide by 5
2/5
Multiply by 3
2/5 x 3 = 1.2
Add this to the x coordinate of J
2 + 1.2 = 2.2

Get the vertical distance:
19 - 5 = 14
Divide by 5
14/5
Multiply by 3
14/5 x 3 = 8.4
Add this to the y coordinate of J
5 + 8.4 = 13.4

The coordinates of the point is
(2.2,13.4)

You can find the area of a rectangle by multiplying the length and height. so multiply 1/2*7/4(which is the simpler version of 1 3/4) and you get 7/8 as your answer.