Q13 of 184 Page 10

Prove that the points (3, 4), (8, - 6) and (13, 9) are the vertices of a right angled triangle.

Given points are A(3, 4), B(8, - 6) and C(13, 9).



Let us find the distance between sides AB, BC and CA.


We know that distance between the two points (x1, y1) and (x2, y2) is .






⇒ AB = √125





⇒ BC = √250





⇒ CA = √125


Now,



⇒ AB2 + CA2 = 125 + 125


⇒ AB2 + CA2 = 250



⇒ AB2 + CA2 = BC2


∴ The given points form a right angled isosceles triangle.


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