Q1.Due to corona virus pandemic students are made to sit in a classroom at a distance of 2mapart from each other Let the position of the 3 students in a class is A(3, 1), B(6, 4) and C(8, 6) .
Find
i)Distance between the students A and C.
ii)Distance between B and C
iii) Are the three students seated in a line? Give reason.
Answers
Given : position of the 3 students in a class is A(3, 1), B(6, 4) and C(8, 6) .
To Find : (i) The distance between A and C
ii)Distance between B and C
iii) Are the three students seated in a line
Solution:
(i) The distance between A and C
A(3, 1) C(8, 6)
= √(8 - 3)² + (6 - 1)²
= √5² + 5²
= 5√2
(ii) The distance between B and C
B(6, 4) C(8, 6)
= √(8 - 6)² + (6 - 4)²
= √2² + 2²
= 2√2
The distance between A and B
A(3, 1) B(6, 4)
= √(6- 3)² + (4 - 1)²
= 3√2
3√2 + 2√2 = 5√2
=> AB + BC = AC
Hence A, B and C are collinear
=> three students seated in a line
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