Question

check whether (5,-2), (6,4)and (7,-2)are vertices of an isosceles triangle

Answer 1

the solution is given in the above page

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption

P = (5 , -2)

Q = (6 , 4)

R = (7 , -2)

$\tt{\rightarrow PQ=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}}$

$\tt{\rightarrow PQ=\sqrt{(6-5)^2+4-(-2)^2}}$

$\tt{\rightarrow PQ=\sqrt{1+36}}$

$\tt{\rightarrow PQ=\sqrt{37}}$

Now

$\tt{\rightarrow QR=\sqrt{(x_{3}-x_{2})^2+(y_{3}-y_{2})^2}}$

$\tt{\rightarrow QR=\sqrt{(7-6)^2+(-2-4)^2}}$

$\tt{\rightarrow QR=\sqrt{1+36}}$

$\tt{\rightarrow QR=\sqrt{37}}$

Now

$\tt{\rightarrow PR=\sqrt{(x_{3}-x_{1})^2+(y_{3}-y_{1})^2}}$

$\tt{\rightarrow PR=\sqrt{(7-5)^2+ -2-(2)^2}}$

$\tt{\rightarrow PR=\sqrt{4+0}}$

= 2

★Therefore

★∆PQR is an isosceles triangle