What is a necessary step for constructing perpendicular lines through a point on a line? Draw a line that intersects the first line at an acute angle using a straightedge.
Draw a ray that intersects the first line at an acute angle using a straightedge.
Draw arcs on either side of a given point on the line.
Draw arcs on either side of a given point off the line.

I uploaded the answer to a file hosting. Here's link:

cutt.ly/nz6VGda

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)