Question

Which type of triangle is formed by joining the vertices A(-3, 6), B(2, 1), and C(9, 5)?

Answer 1

We can determine the type of triangle from the length of the sides. The length of the sides can be found using the distance formula.


`AB= \sqrt{ (2+3)^(2) + (1-6)^(2) } =5 √(2) \\ \\ BC= \sqrt{ (9-2)^(2) + (5-1)^(2) } =√(65) \\ \\ CA = \sqrt{ (-3-9)^(2) + (6-5)^(2) } = √(145) \\ \\`

None of the side lengths are equal, so the triangle formed by the given vertices is a Scalene Triangle. Moreover, the Pythagorean theorem is also not satisfied with given side lengths, so the triangle is NOT a Right Angled Triangle.