Question

If the vertices of a triangle are $(-2,0),(2,3)$ and $(1,-3)$, then the triangle is

• A. scalene
• B. equilateral
• C. isosceles
• D. right triangle

Answer 1

Answer: (A)

scalene

Let the vertices of the triangle be $A(-2,0)$, $B(2,3)$ and $C(1,-3)$.

We compute the length of the sides as follows:

$AB=\sqrt{{(2-(-2\left)\right)}^2+{(3-0)}^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=5$

$BC=\sqrt{{(1-2)}^2+{(-3-3)}^2}=\sqrt{(-1{)}^2+{(-6)}^2}=\sqrt{1+36}=\sqrt{37}$

$AC=\sqrt{{(1-(-2\left)\right)}^2+{(-3-0)}^2}=\sqrt{3^2+{(-3)}^2}=\sqrt{9+9}=\sqrt{18}$

Since none of the lengths of the sides are equal, therefore, it is a scalene triangle.