MathDB

The coordinates of the vertices of isosceles trapezoid

ABCD

are all integers, with

A=(20,100)

and

D=(21,107).

The trapezoid has no horizontal or vertical sides, and

\overline{AB}

and

\overline{CD}

are the only parallel sides. The sum o f the absolute values of all possible slopes for

\overline{AB}

m/n,

where

m

and

n

are relatively prime positive integers. Find

m+n.

Problem Statement