Classify the triangle by its sides a(3,-3), b(1,4), c(-1,-1)

The triangle is scalene Δ

Step-by-step explanation:

* Lets revise the types of the triangle according to its sides

- Equilateral triangle: its three sides are equal in lengths

- Isosceles triangle: two sides are equal in lengths

- Scalene triangle: its three sides have different lengths

- The length of a segment basses through two points (x1 , y1) and

 (x2 , y2) is √[(x2 - x1)² + (y2 - y1)²]

* Lets solve the problem

∵ abc is a triangle with vertices a (3 , -3) , b (1 , 4) , c (-1 , -1)

- To classify the triangle by its side find the lengths of the 3 sides

∵ a = (3 , -3) and b = (1 , 4)

∴ ab = √[(1 - 3)² + (4 - -3)²] = √[(-2)² + (7)²] = √[4 + 49] = √53

∵ b = (1 , 4) and c = (-1 , -1)

∴ bc = √[(-1 - 1)² + (-1 - 4)²] = √[(-2)² + (-5)²] = √[4 + 25] = √29

∵ c = (-1 , -1) , a = (3 , -3)

∴ ca = √[(3 - -1)² + (-3 - -1)²] = √[(4)² + (-2)²] = √[16 + 4] = √20

∵ The lengths of the three sides of the triangle are √53 , √29 , √20

∴ The lengths of the three sides are different

∴ The triangle is scalene Δ

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step-by-step explanation:

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