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Math Help - Equation of a line (Coordinate geometry)

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    Equation of a line (Coordinate geometry)

    Find the equation of a line through (1,3) and forming with the axes a triangle of area 6 square units. (Give three solutions).
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    Hello snigdha
    Quote Originally Posted by snigdha View Post
    Find the equation of a line through (1,3) and forming with the axes a triangle of area 6 square units. (Give three solutions).
    Suppose the line has gradient m. Then its equation is:
    y-1=m(x-3)
    Simplify this, and then find the coordinates of the intercepts. They are:
    \left(\frac{m-3}{m},0\right) and (0, 3-m)
    Then, using \tfrac12 base x height, write down an expression to represent the area of the triangle, and equate this to \pm 6. (You need the \pm sign, because you might have negative distances, and hence a negative area.

    Re-write this as a pair of quadratic equations in m (one equation for each of the two possible signs.)

    Solve these to find the possible values of m, and hence the equations of the lines.
    Spoiler:
    The values of m are m = -3, or 9\pm6\sqrt2


    Grandad
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