Answer:
The triangle is scalene Δ
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