If you take a number, times by 5 then subtract 9. You get the same as if you took the number, times by 4 then add 1. What is the number?

Let number be x

5x + 9= 4x + 1

5x - 4x = - 9 + 1

x = - 8

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)