Prove that the points (0,0), (5,5) (-5,-5) are the vertices of a right angled triangle - Maths - Coordinate Geometry

Question

Prove that the points (0,0), (5,5) & (-5,-5) are the
vertices of a right angled triangle

ramandeep.singh · Accepted Answer

Let A (0, 0), B (5, 5) and C (â€“5, â€“5) be the given points then, $AB = \sqrt{(5 âˆ’ 0)^{2} + (5 âˆ’ 0)^{2}} = \sqrt{25 + 25} = \sqrt{50} = 5 \sqrt{2} units BC = \sqrt{(5 âˆ’ (âˆ’ 5))^{2} + (5 âˆ’ (âˆ’ 5))^{2}} = \sqrt{10^{2} + 10^{2}} = \sqrt{200} = 10 \sqrt{2} units AC = \sqrt{{(âˆ’ 5 âˆ’ 0)}^{2} + (âˆ’ 5 âˆ’ 0)^{2}} = \sqrt{25 + 25} = \sqrt{50} = 5 \sqrt{2} units$ $A B^{2} + A C^{2} = (5 \sqrt{2})^{2} + (5 \sqrt{2})^{2} = 50 + 50 = 100 = B C^{2}$ As $A B^{2} + A C^{2} = B C^{2}$ , therefore, Î”ABC is a right-angled triangle, with âˆ A = 90o

Prove that the points (0,0), (5,5) & (-5,-5) are the vertices of a right angled triangle.