A triangle with vertices (4,0),(-1,-1),(3,5) is:

Question

A triangle with vertices $(4,0),(-1,-1),(3,5)$ is:

Accepted Answer

$$AB = \sqrt {{{\left( {4 + 1} \right)}^2} + {{\left( {0 + 1} \right)}^2}}  = \sqrt {26} ;$$

$$BC = \sqrt {{{\left( {3 + 1} \right)}^2} + {{\left( {5 + 1} \right)}^2}}  = \sqrt {52} $$

$$CA = \sqrt {{{\left( {4 - 3} \right)}^2} + {{\left( {0 - 5} \right)}^2}}  = \sqrt {26} ;$$

In isosceles triangle side $AB=CA$

For right angled triangle, $B{C^2} = A{B^2} + A{C^2}$

So, here $$BC = \sqrt {52} $$ or $B{C^2} = 52$

or $$\,\,\,\,\,\,\,\,\,{\left( {\sqrt {26} } \right)^2} + {\left( {\sqrt {26} } \right)^2} = 52$$

So, the given triangle is right angled and also isosceles.

Solutions · 1