Question

triangle ABC has vertices A(0,0), B(3,3), and C(-3,3). Classify it by its sides. then determine if it is a right triangle.

Answer 1

http://fooplot.com/#W3sidHlwZSI6MywiZXEiOltbIjAiLCIwIl0sWyIzIiwiMyJdLFsiLTMiLCIzIl1dLCJjb2xvciI6IiNEQjFDMUMifSx7InR5cGUiOjEwMDB9XQ--

Answer 2

if segment AB is perpendicular to segment AC
then that means the angle at point A is 90 degrees and thus the triangle would be a right triangle

to find that out, get the slope of AB and then get the slope of AC

perpendicular lines have NEGATIVE RECIPROCAL slopes
so if say \(\bf \textit{slope of }AB\implies \cfrac{a}{{\color{blue}{ b}}}\qquad reciprocal\implies \cfrac{{\color{blue}{ b}}}{a}\qquad negative\implies -\cfrac{{\color{blue}{ b}}}{a}
\\ \quad \\
\textit{so if the slope of }AC\implies -\cfrac{{\color{blue}{ b}}}{a}\)
then angle at point A is indeed perpendicular

Answer 3

to classify it, well check -> http://www.mathsisfun.com/geometry/triangles-interactive.html