I am assuming that the question reads:
"Determine whether the points A(-2, -1) B(2, -2) C(1, -4) are the vertices of an scalene, isosceles, or equilateral triangle."
By the Distance Formula, we see that the lengths of the sides of the triangle are:
(a) AB = √[(-2 - 2)^2 + (-1 + 2)^2] = √17
(b) AC = √[(-2 - 1)^2 + (-1 + 4)^2] = 3√2
(c) BC = √[(2 - 1)^2 + (-2 + 4)^2] = √5.
Since the triangle is neither isosceles nor equilateral, it is scalene.
I hope this helps!
"Determine whether the points A(-2, -1) B(2, -2) C(1, -4) are the vertices of an scalene, isosceles, or equilateral triangle."
By the Distance Formula, we see that the lengths of the sides of the triangle are:
(a) AB = √[(-2 - 2)^2 + (-1 + 2)^2] = √17
(b) AC = √[(-2 - 1)^2 + (-1 + 4)^2] = 3√2
(c) BC = √[(2 - 1)^2 + (-2 + 4)^2] = √5.
Since the triangle is neither isosceles nor equilateral, it is scalene.
I hope this helps!