Answer:
Indeed, the given triangle is a right triangle.
Step-by-step explanation:
A triangle is formed by the following three points: [tex]A(x,y) = (x_{1}, y_{1})[/tex], [tex]B(x,y) = (x_{2}, y_{1})[/tex] and [tex]C(x,y) = (x_{2}, y_{2})[/tex]. Then, we construct the following vectors:
[tex]\overrightarrow {BA} = (x_{2}-x_{1}, y_{1}-y_{1})[/tex]
[tex]\overrightarrow{BA} = (x_{2}-x_{1}, 0)[/tex] (1)
[tex]\overrightarrow{BC} = (x_{2}-x_{2}, y_{2} - y_{1})[/tex]
[tex]\overrightarrow{BC} = (0, y_{2}-y_{1})[/tex] (2)
If triangle ABC is a right triangle, then [tex]\overrightarrow{BA}\,\bullet\,\overrightarrow{BC} = 0[/tex]. By (1) and (2) we have this expression:
[tex](x_{2} - x_{1})\cdot (0) + (0)\cdot (y_{2} - y_{1}) = 0[/tex]
Therefore, the given triangle is a right triangle.
