Find the point that splits segment ef in half if point e is located at (5,-2) and point f is located at (-1,3)

We need to find the midpoint. Let's call the midpoint M where M = (x,y). For now x and y are unknown

To find the x coordinate of the midpoint, we add up 5 and -1 (which are the x coordinates of E and F respectively) and divide by 2
So 5+(-1) = 5-1 = 4 which divided over 2 is 4/2 = 2
The x coordinate of the midpoint is x = 2

Similarly, the y coordinate of M is y = (-2+3)/2 = 1/2 = 0.5

So the midpoint M is (x,y) = (2, 0.5) 

One property of M is that EM = MF. Another property is that EM+MF = EF

Okay for this problem you would need to use the mid-point formula...
It uses the x and y coordinate system (x , y) 
this is how the formula looks like substitute this for the x coordinate (x₁ + x₂)/2 
and this for the y coordinate (y₁ + y₂)/2

Now all you have to do is substitute the values into the right variables...

E (5 , -2)  is (x₁, y₁)
F (-1 , 3) is (x₂ , y₂)

(x₁ + x₂)/2                          (y₁ + y₂)/2
(5 - 1)/2                             (-2 + 3)/2
4/2                                     1/2
2

We now have the x and y coordinate for the mid-point
The answer is... ( drumroll please :D)  
(2, 1/2)

I hope this helps you! :D

Please vote me for brainliest!

10.4 is the answer for you