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18 May, 14:34

Let A = (-2, 6), B = (1, 0), and C = (5, 2). Prove that △ABC is a right-angled triangle. Let u = AB, v = BC, and w = AC. We must show that u · v, u · w, or v · w is zero in order to show that one of these pairs is orthogonal. u · v = Incorrect: Your answer is incorrect. u · w = Incorrect: Your answer is incorrect. v · w = Incorrect: Your answer is incorrect.

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  1. 18 May, 16:18
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    Step-by-step explanation:

    In a triangle ABC, given A = (-2,6),

    B = (1,0) and C = (5,2)

    If u = AB, v = BC, w = AC

    To show that the triangle is a right angled triangle, we must show that the dot product of one of the pairs is zero.

    Since u = AB

    u = AB = B-A

    u = AB = (1,0) - (-2,6)

    u = [ (1 - (-2), 0-6]

    u = (3, - 6)

    Similarly, v = BC = C-B

    v = BC = (5,2) - (1,0)

    v = [ (5-1), (2-0) ]

    v = (4, 2)

    Also for w:

    w = AC = C - A

    w = (5, 2) - (2, - 6)

    w = [ (5-2), (2 - (-6) ]

    w = (3, 8)

    To show that the triangle is a right angled triangle, the dot product of one of any of the pairs must be zero as shown:

    u. v = (3, - 6) • (4, 2)

    u. v = (3) (4) + (-6) (2)

    u. v = 12-12

    u. v = 0

    i. e AB. BC = 0

    This shows that length AB and BC are perpendicular to each other i. e the angle between them is 90° and since a right angled triangle has one of its angle to be 90°, it shows that the ∆ABC is a right angled triangle.
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