31. Sonia and Asha planted some trees in a
square garden as shown in figure. Both
were arguing that they have planted them
in a straight line. Find which of them is
correct. Justify your decision (Here, S
stands for Sonia and A for Asha).
Az (4, 6)
- Noworo
A₂ (3, 47/5₃ (6,5)
A, (2,3)
"S₂ (4,3)
S, (2, 1)
1
2 3
4
5
6
7
8
Answers
Sonia have planted in straight line
Step-by-step explanation:
coordinates of
sonia's plants are: S₁(2,1); S₂(4,3); S₃(6,5) and
asha's plants: A₁(2,3); A₂(3,4); A₃(4,6)
S₁(2,1); S₂(4,3); S₃(6,5)
Slope S₁ & S₂ = (3 - 1)/(4 - 2) = 1
Slope S₁ & S₃ = (5 - 1)/(6 - 2) = 1
Slope S₂ & S₃ = (5 - 3)/(6 - 4) = 1
Same slope
Hence S₁(2,1); S₂(4,3); S₃(6,5) are in a straight line
Sonia have planted in straight line
A₁(2,3); A₂(3,4); A₃(4,6)
Slope A₁ & A₂ = (4 - 3)/(3 - 2) = 1
Slope A₁ & A₃ = (6 - 3/(4 - 2) = 1 .5
Slope A₂ & A₃ = (6 - 4)/(4 - 3) = 2
Slope are different
Hence A₁(2,3); A₂(3,4); A₃(4,6) are not in a straight line
Sonia have planted in straight line
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