seema has a 10 m x 10 m kitchen garden attached to her kitchen. she ides it into a 10 x 10 grid and wants to grow some vegetables and herbs used in the kitchen. she puts some soil and manure in that and shows a green chilly plant at a, a coriander plant at b and a tomato plant at c. her friend kusum visited the garden and praised the plants grown there. she pointed out that they seem to be in a straight line. see the below diagram carefully and answer the following questions :
1) write the coordinates of the points a, b and c taking the 10 x 10 grid as coordinate axes.
2(by distance formula or some other formula, check whether the points are collinear.
Answers
1) A - (2,2)
B - (5,4)
C - (7,6)
2) no the points are not collinear because the three points form a triangle and it has area but collinear point does not have any area.
Answer: 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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