Respuesta :
With the coordinates of the vertices of triangle ABC at A(-1, 3), B(-5, -1), C(3, -1), we have;
- Triangle ABC is an isosceles triangle
How can the type of a given triangle be found?
Taking the vertices of ∆ABC as found in a similar question online as A(-1, 3), B(-5, -1), C(3, -1), calculating the lengths of the sides of the triangle gives;
AB = √((-1 - (-5))² + (3 - (-1))²) = 4•√2
AC = √((-1 - 3)² + (3 - (-1))²) = 4•√2
BC = √((-5 - 3)² + (-1 - (-1))²) = 8
AB = AC = 4•√2
- Triangle ABC is an isosceles triangle by the definition of isosceles triangles.
(AB)² + (AC)² = (4•√2)² + (4•√2)² = 64 = (BC)²
Therefore;
(BC)² = (AB)² + (AC)²
Which indicates that triangle ABC is an isosceles right triangle.
Learn more about the types of triangles here:
https://brainly.com/question/1058720
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