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) are representing 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)  = sqrt37`

`BC = sqrt((6-7)^2+(4-(-2))^2)=sqrt((-1)^2+(6)^2) = sqrt(1+36)= sqrt37`

`CA = sqrt((5-7)^2+(-2-(-2))^2) = sqrt((-2)^2+0^2) = 2`

Therefore AB = BC

As two sides are equal in length, therefore, ABCis an isosceles triangle.