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in Coordinate Geometry by (30.3k points)
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Show that the points A(-5,6), B(3,0) and C(9,8) are the vertices of an isosceles right-angled triangle. Calculate its area.

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Let the given points be A(-5,6) B(3,0) and C(9,8).

Therefore, AB = BC = 10 units

This show that \(\triangle ABC\) is right angled at B.

Therefore, the points A(-5,6) B(3,0) and C(9,8) are the vertices of an isosceles rightangled triangle

Also, area of a triangle = \(\frac{1}{2}\times base\times height\)

If AB is the height and BC is the base,

\(Area=\frac{1}{2}\times 10\times 10\)

= 50 square units

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