Show that the lines OA and OB are perpendicular,where A,B and O are the points (5,4),(4,-5) and (0,0) respectively.

Distance between O and A
whole root(5-0)2+(4-0)2=root 41
Distance between O and B
whole root(4-0)2+(-5-0)2=root 41
Distance between A and B
whole root(5-4)2+(4+5)2=root 82


checking perpendicular..
OA+OB2=AB2
(root 41)2+(root 41)2=AB2
41+41=AB2
82=AB2
AB=root82
which is equal to the calculated distance of AB by the distance formula.
this proves that OA and OB are perpendicular.


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