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

Question

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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Kaylee 2 weeks 2021-11-21T12:49:47+00:00 1 Answer 0 views 0

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    2021-11-21T12:51:00+00:00

    Answer:

    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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