Question

Classify the triangle defined by the points A(3,-4), B(5,-1), C(6,-2) as equilateral, isosceles, or scalene.

Answer 1

`\overline{AB}=√((5-3)^2+(-1-(-4))^2)=√(4+9)=√(13)\\ \overline{AC}=√((6-3)^2+(-2-(-4))^2)=√(9+4)=√(13)\\ \overline{BC}=√((6-5)^2+(-2-(-1))^2)=√(1+1)=√(2)\\`

The triangle has exactly two sides of the same length, so it's isosceles triangle.