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in Coordinate Geometry by (41.6k points)
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Check whether the points (3, 0), (6,4) and (—1, 3) are the vertices of a right – angled isosceles triangle or not. Also find the area of the triangle.

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Distance between A(3, O), B(6, 4)

∴ AB2 = 25, BC2 = 50, CA2 = 25 

BC2= AB2 + CA2 and AB = CA 

∴ ∆ ABC is an Isosceles right angled triangle 

∴ Area of ∆ABC = \(\frac{1}{2}\) x AB x AC 

= \(\frac{1}{2}\) x 5 x 5 = 12.5sq.u

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