Prove that the points A(7,10);B (-2,5);and C(3,-4) are the vertices of isosceles Right triangle

Prove that the points A(7,10);B (-2,5);and C(3,-4) are the vertices of

1.	Prove that the points A(7,10);B (-2,5);and C(3,-4) are the vertices of isosceles Right triangle
Answer» Let A(7,10),B(-2,5) and C(3,-4) be the vertices of given isosceles triangle.Then,\xa0{tex}AB=\\sqrt{(7+2)^2+(10-5)^2}=\\sqrt{106}{/tex}{tex}AC=\\sqrt{(7-3)^2+(10+4)^2}=\\sqrt{212}{/tex}{tex}BC=\\sqrt{(3+2)^2+(-4-5)^2}=\\sqrt{106}{/tex}Thus,AB=ACHence, given vertices are coordinates of an isosceles triangle.