Anjali,arun and arjun sat at positions (2,-5) , (4,-1) , (1,2) respectively then show that they are lie on same line
Answers
Answer:
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Given : Anjali, arun and arjun sat at positions (2,-5) , (4,-1) , (1,2) respectively
To Find : show that they are lie on same line
Solution:
Method 1 : Equal slope
if slope between pair of any two points is same then points are colinear
(2,-5) , (4,-1) , (1,2)
(2,-5) , (4,-1) slope = ( -1 + 5)/( 4 -2 ) = 4/2 = 2
(2,-5) (1,2) slope = ( 2 + 5) / ( 1 - 2) = 7/-1 = -7
slopes are not equal hence points does not lie on same line
Method 2 : if points are on same line
then area formed by triangle with points = 0
(2,-5) , (4,-1) , (1,2)
=> (1/2) | 2 (-1 - 2) + 4(2 + 5) + 1 (-5 + 1) |
= (1/2) | -6 + 28 - 4 |
= 9
≠ 0
Hence points does not lie on same line
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