The points (1,1), (-2, 7) and (3, -3) are ______. - Mathematics

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MCQ
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The points (1,1), (-2, 7) and (3, -3) are ______.

Options

  • vertices of an equilateral triangle

  • collinear

  • vertices of an isosceles triangle

  • none of these

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Solution

The points (1,1), (-2, 7) and (3, -3) are collinear.

Explanation:

Let A(1, 1), B(-2, 7) and C(3, 3) are the given points, Then, we have

AB = `sqrt((- 2 - 1)^2 + (7 - 1)^2) = sqrt(9 + 36) = sqrt45 = 3sqrt5`

BC = `sqrt((3 + 2)^2 + (- 3 - 7)^2) = sqrt(25 + 100) = sqrt125 = 5sqrt5`

and AC = `sqrt((3 - 1)^2 + (- 3 - 1)^2) = sqrt(4 + 16) = sqrt20 = 2sqrt5`

Clearly BC = AB + AC.

∴ A, B, C are collinear.

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