Question

Identify the points $(3,0),(6,4)$ and $(-1,3)$ are the vertices of which triangle.

• A. Scalene triangle
  
• B. Right angled isosceles triangle
  
• C. Acute angled triangle
  
• D. obtuse angled triangle
  

Answer 1

Answer: (B)

Right angled isosceles triangle

Given points are $(3,0),(6,4)$ and $(-1,3)$

Now, $AB=\sqrt{{(6-3)}^2+{(4-0)}^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}$

$BC=\sqrt{-{(1-6)}^2+{(3-4)}^2}=\sqrt{{(-7)}^2+{(-1)}^2}=\sqrt{49+1}=\sqrt{50}$

$AC=\sqrt{{(-1-3)}^2+{(3-0)}^2}=\sqrt{{(-4)}^2+{\left(3\right)}^2}=\sqrt{16+9}=\sqrt{25}$

Since, $AB=BC$

Thus, $A{B}^2+A{C}^2=B{C}^2$

Hence, $△ABC$ is an right-angled isosceles triangle.