find the coordinates of the midpoint of segment hx h(5(1/2),-4(1/4)) x(3(3/4), -1(1/4))

First simplify the point coordinates to make this easier to look at/solve.

Point h:

(5(1/2),-4(1/4))

(5/2),(-4/4))

(5/2),(-1)

Point x:

(3(3/4), -1(1/4))

(9/4),(-1/4)

Now we have to use the midpoint formula, which basically adds the x values of both points, then divides them by 2.

You then do this to the y values too. Here's a picture showing you the midpoint formula:

Let's put in the values of your two points:

$$(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$$

$$(\frac{\frac{5}{2} + \frac{9}{4}}{2},\frac{-1 + -\frac{1}{4}}{2})$$

$$(\frac{\frac{10}{4} + \frac{9}{4}}{2},\frac{-\frac{4}{4} + -\frac{1}{4}}{2})$$

$$(\frac{\frac{19}{4}}{2},\frac{-\frac{5}{4}}{2})$$

$$({\frac{19}{4}}\times\frac{1}{2},{-\frac{5}{4}}\times\frac{1}{2})$$

$$({\frac{19}{8}},{-\frac{5}{8})$$

Looks like the midpoint is  $$(\frac{19}{8}, -\frac{5}{8})$$  or  $$(2\frac{3}{8}, -\frac{5}{8})$$

Picture taken from: http://www.regentsprep.org/Regents/math/geometry/GCG2/Lmidpoint.htm