Question 1045545
A vector associated with the points (-1,-2) and (5,4) is < 5--1, 4--2 > = < 6, 6 >.

A vector associated with the points (-1,-2) and (-3,0) is < -3--1,0--2 > = < -2,2 >.

Two vectors are perpendicular (or orthogonal) if their dot product is 0, 

< 6,6 >*<-2,2 > = -12 + 12 = 0.

This, however, is not a new way, just a little level higher.  

Another way of showing this perpendicularity, but still not a "new" way, just a level lower, is 
getting the slope of the line passing through (-1,-2) and 
(5,4) and comparing this with the slope of the line passing through (-1,-2) 
and (-3,0).