Seema has 10 into 10 metre kitchen garden attached to a kitchen she divides it into a time in 213 grade and wants to grow some vegetables and Herbs used in the kitchen she put some soil and Manual in that and shows the green chilli plant I take a coriander plant at B and tomato plant at see her friend Kusum visited the garden and press the plants grown there she pointed out they seem to be in a straight line see the below diagram carefully and answer the following questions write the coordinates of point A B and C taking the 10 into 10 grade as coordinate Axis at a distance formula or some other formula check whether the points are collinear
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Seema has a 10 m x 10 m kitchen garden . Coordinates of herb grown are given in attached graph
To find : Whether plants grown are in straight line or not
Solution:
A = (2 , 2)
B = (5 , 4)
C = ( 7 , 6)
Slope AB = ( 4 - 2)/(5 - 2) = 2/3
Slope of AC = ( 6 - 2)/(7 - 2) = 4/5
Slope of BC = ( 6 - 4)/(7 - 5) = 2/2 = 1
Slopes are not equal
hence points are not in a straight line
Hence points are not collinear
AB = √(5 - 2)² + (4 - 2)² = √13
BC = √(7 - 5)² + (6 - 4)² = 2√2
AC = √(7 - 2)² + (6 - 2)² = √41
AB + BC ≠ AC
=> A , B & C are not in straight line
points are not collinear
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