see attachment
if you move the whole triangle up 4 units and to the left 3 units without rotating or dialating it, then each point should move up 4 units and 3 units to the left
find the distance between the first point and the translated point
if we draw out the path, we can see that the path makes 2 legs of a right triangle. the distance between the start and end is the hypotonuse
the 2 legs are length 3 and 4
by the pythagorean theorem, d²=3²+4²
d²=9+16
d²=25
d=5
so the distance between any 2 points on the original triangle and the translated triangle is 5 units
