Check weather (5,-2)(6,4)and(7,-2)are vertices of isosceles …
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Yogita Ingle 7 years, 1 month ago
Let the points (5, - 2), (6, 4), and (7, - 2) are representing the vertices A, B, and C of the given triangle respectively.
AB = {tex}\;\sqrt{{(5-6)}^2+\;(-2-4)^2}\;=\;\sqrt{(-1)^2\;+\;(-6)^2}\;=\;\sqrt{1\;+36\;}\;=\sqrt{37}{/tex}
BC = {tex}\;\sqrt{{(6-7)}^2+\;(4\;-\;(-2))^2}\;=\;\sqrt{(-1)^2\;+\;(6)^2}\;=\;\sqrt{1\;+36\;}\;=\sqrt{37}{/tex}
CA = {tex}\;\sqrt{{(5-7)}^2+\;(-2)\;-\;(-2))^2}\;=\;\sqrt{(-2)^2\;+\;(0)^2}\;=\;\sqrt{4\;}\;=2{/tex}
Therefore, AB = BC
As two sides are equal in length, therefore, ABC is an isosceles triangle.
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