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Prove that by joining the points (2, 1), (3, 4), (-3, 6) we get a right triangle. |
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Answer» Let, A(2, 1), B(3, 4), C(-3, 6) be the vertices of the triangle ABC. AB = \(\sqrt{(3-2)^2+(4-1)^2}\) = \(\sqrt{1^2+3^2}=\sqrt{10}\) BC = \(\sqrt{(-3-3)^2+(6-4)^2}\) = \(\sqrt{6^2+2^2}=\sqrt{40}\) AC = \(\sqrt{(2-3)^2+(1-6)^2}\) = \(\sqrt{5^2+(-5)^2}=\sqrt{50}\) Using Pythogoras theorem AC2 = AB2 + BC2 50 = (√10)2 + (√40)2 = 50 ∴ We obtain a right triangle. |
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