Given vertices of triangle ABC are A(−1, 4) , B(3, 1) , and C(0,−3).
Slope of AB is :
[tex]m=\frac{1-4}{3-\left(-1\right)} = -\frac{3}{4}[/tex]
Slope of BC is :
[tex]m=\frac{-3-1}{0-3}=\frac{4}{3}[/tex.
Slope of AC is:
[tex]m=\frac{-3-4}{0-\left(-1\right)}=-7.[/tex]
Slope of AB is negative reciprocal of slope of BC.
Therefore, AB and BC are perpendicular lines and triangle ABC is a right triangle.
The slope of AB is -3/4, the slope of BC is 4/3, and the slope of AC is -7. Triangle ABC is a right triangle because two of these slopes have a product of -1.
