Question

show the following points taken in order form an isosceles triangle.A(5,4),B(2,0),C(-2,3)

Answer 1

Answer: Showed.

Step-by-step explanation: The given points are A(5,4), B(2,0) and C(-2,3).

We all know the types of triangles in geometry. For example equilateral triangle has all sides equal, isosceles triangle has two sides equal and a scalene triangle has no sides equal.

Thus, to show the points A, B and C will make an isosceles triangle, we need to show the length of any two of them equal.

Now,

$AB=\sqrt{(5-2)^2+(4-0)^2} = \sqrt{9+16}=\sqrt{25}=5~units,\\\\BC=\sqrt{(2+2)^2+(0-3)^2} = \sqrt{16+9}=\sqrt{25}=5~units,\\\\CA=\sqrt{(-2-5)^2+(3-4)^2} = \sqrt{49+1}=\sqrt{50}=5\sqrt2~units.$

Since AB=BC, so Δ ABC is an isosceles triangle.