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Math Help - Trigonometry Question

  1. #1
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    Trigonometry Question

    Being a triangle and a point inside .
    Find the coordinates of the points and on the sides of , in function of the coordinates of the points and , in a way that divides the line segment in half.
    (Tip: Consider the point to be on the origin of the coordinates system and point to be on the axis.)
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  2. #2
    Member kalyanram's Avatar
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    Re: Trigonometry Question

    Hey Don,
    Refer to the figure attached. Choose x-axis along AB and y-axis along AC with the origin at A.

    Q,R can be interchanged.

    Case 1.
    QR on sides AB and AC we have Q=(2\alpha,0), R=(0,2\beta). With the additional condition that 0 \le \alpha \le \frac{b}{2}, 0 \le \beta \le \frac{c}{2}

    Case 2.
    QR on sides AC and BC we have the abscissa of Q is 0 and hence abscissa of R has to be 2\alpha. Let the ordinate of Q be \gamma then we have ordinate of R has to be 2\beta-\gamma and it has to satisfy the line equation \frac{y}{x-b} = -\frac{c}{b} \implies \gamma = -\frac{c(2\alpha - b)}{b} with the additional bound constraints 0 \le \alpha \le \frac{b}{2} and 0 \le \gamma \le c

    Case 3.
    Can be done on similar lines of Case2.

    Now use the rotational matrix to translate to the Rectangular Cartesian Co-ordinates.

    ~Kalyan.
    Attached Thumbnails Attached Thumbnails Trigonometry Question-pintri.png  
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