Answer:
RST is not an equilateral
Step-by-step explanation:
Given
[tex]R = (-2,-2)[/tex]
[tex]S = (1,4)[/tex]
[tex]T = (4,5)[/tex]
Required
Prove or disprove the triangle is equilateral
To do this, we simply calculate the distance between each vertex using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]RS = \sqrt{(-2 - 1)^2 + (-2 - 4)^2}[/tex]
[tex]RS = \sqrt{45}[/tex]
[tex]ST = \sqrt{(1 - 4)^2 + (4 - 5)^2}[/tex]
[tex]ST = \sqrt{10}[/tex]
[tex]RS \ne ST[/tex] means the triangle is not an equilateral
