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in Geometry and Algebra by (30.8k points)
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Prove that A(6, 4), B(5, –2), C(7, –2) are the vertices of an isosceles triangle. If D is the midpoint of the side BC ,find the coordinates of D. Calculate the length of this median. Also, find the coordinates of centroid

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A(6, 4), B(5, -2), C(7, -2) are the verteces of a isosceles triangle AB = AC

∆ ABC is a isosceles triangle, so the coordinates of D is \((\frac{5+7}{2},\frac{-2+-2}{2})=(6,-2)\) D(6, -2).

Length of AD = \(\sqrt{(6-6)^2+(4+2)^2}=6\)

Centroid divide AD in the ratio of 2 : 1

\((\frac{18}{3},\frac{0}{3})\)

Centroid (6, 0)

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