# Without using the Pythagoras theorem, show that the points(4, 4), (3,5) and (-1, -1) are the vertices of a right angled triangle.

Let the vertices be A(4, 4), B(3, 5) and C(-1, -1)

Slope of AB, m1 = = = -1

Slope of BC, m2 = = = Slope of AC, m3 = = 1

Now m1m3 = -1 × (1) = -1

Thus AB ⊥ AC or ∠ A = 900

Hence Δ ABC is a right angled triangle.

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