Q20 of 84 Page 114

Can you draw a triangle with vertices (1, 5), (5, 8) and (13, 14)? Give reason.

Formula used:


Let the points A (1, 5) B (5, 8) and C (13, 14)


Distance of AB


⇒ AB = √ ((5 – 1)2 + (8 – 5)2)


⇒ AB = √ ((4)2 + (3)2)


⇒ AB = √ (16 + 9)


⇒ AB = √ 25


⇒ AB = 5


Distance of BC


⇒ BC = √ ((13 – 5)2 + (14 – 8)2)


⇒ BC = √ ((8)2 + (6)2)


⇒ BC = √ (64 + 36)


⇒ BC = √ 100


⇒ BC = 10


Distance of AC


⇒ AC = √ ((13 – 1)2 + (14 – 5)2)


⇒ AC = √ ((12)2 + (9)2)


⇒ AC = √ (144 + 81)


⇒ AC = √ 225


⇒ AC = 15


Now, we can see that AB + BC = AC.


∴ A, B and C are collinear. Hence, we cannot draw triangle using these coordinates.


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