22. If the points AC(-2, 1), B(a, b) and C(4,-1) are collinear and a -b 1, find the values of a and b
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A= (-2,1) B = (a,b) C = (4,-1)
If points A,B and C are collinear it means that A ,B and C lie on the same plane
Slope of AB = Slope of AC = Slope of BC
Slope Of AB = (b-1)/(a-(-2)) = (b-1)/(a+2)
Slope of AC = (-1-1)/(4-(-2)) = -2/6 = -1/3
==> b-1 / a+2 = -1 / 3
==> b-1 = -1 ==> b = 0
==> a+2 = 3 ==> a = 1
Therefore , a = 1 and b= 0
If points A,B and C are collinear it means that A ,B and C lie on the same plane
Slope of AB = Slope of AC = Slope of BC
Slope Of AB = (b-1)/(a-(-2)) = (b-1)/(a+2)
Slope of AC = (-1-1)/(4-(-2)) = -2/6 = -1/3
==> b-1 / a+2 = -1 / 3
==> b-1 = -1 ==> b = 0
==> a+2 = 3 ==> a = 1
Therefore , a = 1 and b= 0
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