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.

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

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.