Question

The points $A(2,-2),B(-1,2)$ and $C(3,5)$ are vertices of a

• A. acute angle triangle
• B. right angle triangle
• C. obtuse angle triangle
• D. equilateral triangle

Answer 1

The correct option is B right angle triangle

Given points are $A(2,-2),B(-1,2)$ and $C(3,5)$
Side lengths are
$AB=\sqrt{(2+1{)}^2+(-2-2{)}^2}=5\text{units}BC=\sqrt{(-1-3{)}^2+(2-5{)}^2}=5\text{units}AC=\sqrt{(2-3{)}^2+(-2-5{)}^2}=5\sqrt{2}\text{units}$
By observation we write
$A{B}^2+B{C}^2=A{C}^2$
So, $△ABC$ is right angle triangle.