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Coordinate Geometry
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07/06/2021 1:33 pm
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Check whether (5, -2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
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07/06/2021 1:38 pm
Let the points (5, -2), (6, 4), and (7, -2) are representing the vertices A, B, and C respectively.
AB = \(\sqrt{(6-5)^2 + (4+2)^2}\)
= \(\sqrt{(-1)^2 + (6)^2}\)
= \(\sqrt{37}\)
BC = \(\sqrt{(7-6)^2 + (-2-4)^2}\)
= \(\sqrt{(-1)^2 + (6)^2}\)
= \(\sqrt{37}\)
CA = \(\sqrt{(7-5)^2 + (-2+2)^2}\)
= \(\sqrt{(-2)^2 + (0)^2}\)
= 2
Here AB = BC = \(\sqrt{37}\)
This implies, whether given points are vertices of an isosceles triangle.