Question 78895
This is a lovely problem to do for me since I have not done it in a long time

The wonderful thing about coordinates is that all your x lines and your y lines are parallel and perpendicular.  

The horizontal distance in x between those points (-5,6) and (4,-6) is 9 
(or 4 - (-5))  and the vertical difference is 12 (which is 6 - (-6)).   I do not even care in this whether I get the sign wrong,

The next thing I am going to do is use the pythagorean theorem or the distance formula.  The pythagorean theorem says we have a right triangle, one leg is 9 and another leg is 12

12^2 + 9^2 = 144 + 81 = 225 = 15^2

Those two points are 15 units apart  I guar-un-tee it!

The boring distance formula tells you

{{{ d = sqrt( (x1 - x2)^2 + (y1 - y2)^2 ) }}} which is the same thing.