Question

Check the points (5,-2),(6,4) and (7,-2) are the vertices of isosceles triangle

Answer 1

The let vertices of triangle is $A(5,-2),B(6,4)$ and $C(7,-2)$
$\begin{array}{cc}AB& =\sqrt{(6-5{)}^2+(4+2{)}^2}\\ & =\sqrt{1+36}\end{array}$
$=\sqrt{37}$ unit
$\begin{array}{cc}BC& =\sqrt{(7-6{)}^2+(-2-4{)}^2}\\ & =\sqrt{1+36}\\ & =\sqrt{37}\text{unit}\\ CA& =\sqrt{(5-7{)}^2+(-2+2{)}^2}\\ & =\sqrt{4+0}\\ & =2\text{unit}\end{array}$
It is clear $AB=BC=\sqrt{37}$
Hence, These points are the vertices of the isosceles triangle.