Question

The triangle whose vertices are the points $A(0,-1),B(2,1),C(-4,3)$ is:

• A. a scalene triangle.
• B. a right angled isosceles triangle
• C. an isosceles triangle
• D. a right angled triangle

Answer 1

Answer: (D)

a right angled triangle

Three points $A$, $B$ and $C$ are the vertices of right angled triangle if $(AB{)}^2+(AC{)}^2=(BC{)}^2$.

Therefore, we calculate:

$AB=\sqrt{{(2-0)}^2+{(1+1)}^2}=\sqrt{2^2+2^2}=\sqrt{4+4}=\sqrt{8}$

$BC=\sqrt{{(-4-2)}^2+{(3-1)}^2}=\sqrt{(-6{)}^2+(2{)}^2}=\sqrt{36+4}=\sqrt{40}$

$AC=\sqrt{{(-4-0)}^2+{(3+1)}^2}=\sqrt{(-4{)}^2+(4{)}^2}=\sqrt{16+16}=\sqrt{32}$

Since, ${\left(\sqrt{8}\right)}^2+{\left(\sqrt{32}\right)}^2={\left(\sqrt{40}\right)}^2\Rightarrow 8+32=40$ that is $(AB{)}^2+(AC{)}^2=(BC{)}^2$.

Hence, the given points are the vertices of right angled triangle. .