Question

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

Answer 1

step 1 :- find slope of OA and OB
slope of line OA = ( 0 -4)/(0-5)= 4/5

slope of line OB = ( 0+5)/(0-4)= -5/4

step 2:- two line are perpendicular upon each other when multiplication of slopes of given lines is equal to -1

now,

slope of OA × slope of OB = 4/5 × -5/4 = -1


here we see multiplication of slopes = -1
so, OA and OB lines are perpendicular upon each other .