In a colony, three friends Kiran, Manoj and Prakash resides at point A,B and C respectively.The houses
of Kiran and Manoj are in I quadrant and all three houses
are collinear.
and
(a)
IfA(5.8), B(1,4) and C (x, 2) then find the value of x
(b)
In which quadrant does Prakash's house lie?
Answers
Answer:
-1
Use the property if given three collinear points,area of triangle formed is zero
Step-by-step explanation:
x = -1 if all three houses are collinear. A (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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