Question

if the points P(-3,9),Q(a,b)and R(4,-5)are collinear and a+b=1,then find the values of a and b

Answer 1

given,
slope of PQ=slope of QR
b-9/a+3=-5-b/4-a
b-9(4-a)=-5-b(a+3)
4b-ab-36+9a=-5a-15-ab-3b
4b+3b+9a+5a-36+15=0
7b+14a-21=0
7(2a+b-3)=0
2a+b-3=0
2a+b=3..................(1)
a+b=1..............(2)
(1)-(2)=>a=2
substitute a=2 in (2)
2+b=1
b=-1

a=2 and b=-1

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