In a colony, three friends Kiran, Manoj and Prakash resides at points A, B and C respectively of Kiran and Manoj are in A quadrant and all three houses are collinear. IfA (5, 8), B (1, 4) and C (x, 2) then find the value of x.
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x = -1 all three houses are collinear. IfA (5, 8), B (1, 4) and C (x, 2)
Step-by-step explanation:
A ( 5 , 8) , B ( 1, 4) C ( x , 2)
all three houses are collinear
=> Slope of AB = Slope of BC = SLope of AC
Slope of AB = (4 - 8)/(1 - 5) = -4/-4 = 1
Slope of BC = (2 - 4)/(x - 1) = - 2/(x -1) = 2/(1 - x)
2/(1 - x) = 1
=> 1 - x = 2
=> x = - 1
Slope of AC = (2 - 8)/(x - 5) = -6/(x - 5) = 6/(5 - x)
= 6/(5 - (-1)) = 6/6 = 1 ( verified)
x = -1
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