Consider the attached image.
We know how to compute the length of horizontal or vertical segments. In fact, their extreme points share a common coordinate, and their length is given by the absolute difference of the non-constant coordinate.
So, to compute the length of an oblique segment, you can build a right traingle whose legs are horizontal and vertical, so that you can easily compute their length, and use the Pythagorean theorem for the hypotenuse, which is the segment you're interested in.
Since the point R in the figure has coordinate (1,5), you can check that we have PR = 3 and RQ = 4. So, you can get PQ by
[tex] \overline{PQ} = \sqrt{3^2+4^2} = \sqrt{9+16} = \sqrt{25} = 5 [/tex]
