Question

show that the following points A ( 7, 10 ) , B ( -2, 5 ) , C ( 3, -4 ) are the vertices of a right angled triangle.​

Answer 1

Answer:

Let the given points be A(7, 10), B(-2, 5) and C(3, -4), then

AB2 = (-2 - 7)2 + (5 - 10)2

⇒ AB2 = (-9)2 + (-5)2

⇒ AB2 = 81 + 25 = 106

BC2 = {3 - (-2)}2 + (-4 -5)2

⇒ BC2 = (3 + 2)2 + (-4 - 5)2

⇒ BC2 = (5)2 + (-9)2

⇒ BC2 = 25 + 81 = 106

and CA2 = (7 - 3)2 = {10 - (-4)}2

⇒ CA2 = (4)2 + (10 + 4)2

⇒ CA2 = (4)2 + (14)2 = 16 + 196 = 212

Now,

AB2 + BC2 = 106 + 106

⇒ AB2 + BC2 = 212 = CA2

∴ ∠B = 90°

[By converse of Pythagoras theorem]

and AB = BC

Hence, A, B and C are the vertices of isosceles right angle triangle.

Answer 2

Answer:

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