triangle ABC has vertices A(5, 12) B(13, 13) and C (11,5). show that the triangle ABC is. scalene triangle

AB =√( (13 - 5)² + (13-12)²) = √(8² + 1²) = √65

BC = √( (13 - 11)² + (13-5)²) = √(2² + 8²) = √68

AC =√( (11 - 5)² + (5-12)²) = √(6² + 7²) = √85

AB ≠ BC ≠ AC ∴ ABC is Scalene

Step-by-step explanation:

A scalene triangle is a triangle in which all the sides are different lengths.

In order to prove that ABC is scalene, we need to calculate the sidelengths and show them to be different.

The line between points A(x₁, y₁) and B(x₂, y₂) can be denoted AB.

the difference in x-coordinate is x₂ - x₁, and the difference in y-coordinates is y₂ - y₁.

this forms a triangle of length x₂ - x₁ and height y₂ - y₁ and the hypotenuse AB can be calculated using pythagoras' theorem:

AB = √((x₂ - x₁)² +(y₂ - y₁)²)

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