Question

Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

Answer 1

Let the points (5, −2), (6, 4), and (7, −2) represent the vertices A, B, and C of the given triangle respectively.
AB=\(\sqrt{(5-6)^2+(-2-4)^2}=\sqrt{(-1)^2+(-6)^2}=\sqrt{1+36}=\sqrt{37}\)
BC=\(\sqrt{(6-7)^2+(4-(-2))^2}=\sqrt{(-1)^2+(6)^2}=\sqrt{1+36}=\sqrt{37}\)
CA=\(\sqrt{(5-7)^2+(-2-(-2))^2}=\sqrt{(-2)^2+0}=2\)
Therefore, AB=BC
As two sides are equal in length, therefore, ABC is an isosceles triangle.