Question

Are the points $(5,3),(2,9)$ and $(-8,4)$ are vertices of

• A. a right angled triangle.
• B. an isosceles triangle.
• C. a scalene triangle
• D. None of the above

Answer 1

The correct option is A a right angled triangle.

Let points $A(5,3),B(2,9)$ and $C(-8,4)$ are vertices of right angled triangle.
$A{B}^2=(5-2{)}^2+(3-9{)}^2=9+36=45$
$B{C}^2=(2+8{)}^2+(9-4{)}^2=100+25=125$
$C{A}^2=(5+8{)}^2+(3-4{)}^2=169+1^2=170$
$A{B}^2+B{C}^2=C{A}^2$
It is a right angled triangle's vertices.

So, option A is correct.