Prove that (2, -2), (-2, 1) and (5, 2) are the vertices of a right angled triangle. Find the area of the triangle and the length of the hypotenuse.
Vertices of a triangle ABC are: A(2, -2), B(-2, 1) and C(5, 2)
Length of side AB =
Length of side AB =
= 
= 
units
Length of side BC =
= 
= 
units
Length of side AC =
= 
= 
units
Since AB = AC, therefore triangle is an isosceles.
BC2 = AB2 + AC2
(√50)2 = (√25)2 + (√25)2
50 = 25 + 25
50 = 50
Since BC2 = AB2 + AC2; therefore given triangle is right angled triangle.
Area of right angled triangle = 
Area of right angled triangle = 
square units
Length of hypotenuse (BC) = 
= 
units
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