The image shows the arrangement of desks in a classroom. Ashima, Bharti and Camella are seated at A (3, 1), B (6,4) and C (8,6) respectively. Do you think they are seated in a line? Give reasons for your answer ?
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Step-by-step explanation:
A(3,1), B(6,4), C(8,6)
By distance formula
AB = √(6 - 3)² + (4 - 1)²
= √3² + 3²
= √ 9 + 9 = √18 = 3√2
BC = √(8 - 6)² + (6 - 4)²
= √ 2² + 2² = √4 + 4 = √8 = 2√2
AC = √(8 - 3)² + (6 - 1)²
= √ 5² + 5² = √25 + 25 = √50 = 5√2
Longest side is AC = 5√2
AB + BC = 3√2 + 2√2
= 5√2 = AC
Therefore, we can say that they are seated in a straight line
Why? → When the sum of the 2 smaller sides is equal to the value of the longest side, we can say that the result is a straight line.
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