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Math Help - Triangles and graphs

  1. #1
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    Triangles and graphs

    a) prove that the triangle with the vertices at the points:

    A (2,1)
    B(4,5)
    C(0,7)

    is right angled


    b) calculate the area of this triangle

    thanks for any help
    x
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  2. #2
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    Quote Originally Posted by pop_91 View Post
    a) prove that the triangle with the vertices at the points:

    A (2,1)
    B(4,5)
    C(0,7)

    is right angled


    b) calculate the area of this triangle

    thanks for any help
    x
    to a)

    Calculate the slope of AB and BC:

    m_{AB}=\dfrac{5-1}{4-2}= 2

    m_{BC}=\dfrac{5-7}{4-0}=-\frac12

    Since m_{AB} \cdot m_{BC} = -1 ~\implies~AB \perp BC

    to b)
    A right triangle is a half rectangle. Therefore the area of the triangle is:

    a_{ABC} = \frac12 \cdot AB \cdot BC

    Use the distance formula to calculate the length of the sides:

    AB=\sqrt{(4-2)^2+(5-1)^2}=2\sqrt{5}

    BC=\sqrt{(4-0)^2+(5-7)^2}=2\sqrt{5}

    Therefore

    a_{ABC} = \frac12 \cdot 2\sqrt{5} \cdot 2\sqrt{5} = 10
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