Q12 of 46 Page 1

If A(– 2, 2), B(5, 2) and C(k, 8) are the vertices of a right-angled triangle ABC with ∠ B = 90°, then find the value of k.

Given: ABC is a right triangle with ∠ B = 90°


and A(– 2, 2), B(5, 2) and C(k, 8)


To find: Value of k


Proof: In ΔABC, Using Pythagoras theorem


(Hypotenuse)2 = (Perpendicular)2 + (Base)2


(AC)2 = (AB)2 + (BC)2


⇒ (5)2 = (4)2 + OR2


⇒ 25 = 16 + OR2


⇒ OR2 = 25 – 16


⇒ OR2 = 9


⇒ OR = √9


⇒ OR = 3


∴ OR = 3cm


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