Question

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Ashima, Bharti and camella are seated at A(3,1), B(6,4) and C(8,6) respectively. Do think they an seated is a line? Give reasons for your answer.





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Answer 1

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Ashima, Bharti and camella are seated at

A(3,1), B(6,4) and C(8,6) respectively. Do think they an seated is a line? Give reasons for your answer.

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i)

$ab \: = \sqrt{(6 - 3) {}^{2} + (4 - 1) {}^{2} } = \sqrt{(3) {}^{2} + (3) {}^{2} }$

$= \sqrt{9 + 9} = \sqrt{18}$

$= 3 \sqrt{2} units$

$bc \: = \sqrt{(8 - 6) {}^{2} + (6 - 4) {}^{2} }$

$\sqrt{(2) { }^{2} + (2) {}^{2} }$

$= \sqrt{4 + 4} = \sqrt{8}$

$= 2 \sqrt{2} units$

$ac = \sqrt{(8 - 3) {}^{2} + (6 - 1) {}^{2} }$

$= \sqrt{(5) {}^{2} + (5) {}^{2} }$

$= \sqrt{25 + 25}$

$= \sqrt{50}$

$= 5 \sqrt{2}$

AB + BC

$= 3 \sqrt{2} + 2 \sqrt{2}$

=AC

thus Ashima, Bharti and camella are seating at line

ii) co - ordination geometry

iii) democratic values lead to equality

Answer 2

Given :- Ashima, Bharti and camella are seated at A(3,1), B(6,4) and C(8,6) respectively. Do think they an seated is a line ?

Answer :-

we know that, distance between (x1,y1) and (x2,y2) is ,

• √(x2 - x1)² + (y2 - y1)²

so,

→ 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 .

as we can see that,

→ AC = AB + BC

→ 5√2 = 3√2 + 2√2

→ 5√2 = 5√2 .

therefore, we can conclude that, Ashima, Bharti and camella are seated in a line and Bharti is between Ashima and camella .

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