Mathematics

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

$\overline{AB}=\sqrt{(5-3)^2+(-1-(-4))^2}=\sqrt{4+9}=\sqrt{13}\\ \overline{AC}=\sqrt{(6-3)^2+(-2-(-4))^2}=\sqrt{9+4}=\sqrt{13}\\ \overline{BC}=\sqrt{(6-5)^2+(-2-(-1))^2}=\sqrt{1+1}=\sqrt{2}\\$ The triangle has exactly two sides of the same length, so it's isosceles triangle.