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Math Help - Urgent Finding Coordinates

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    Post Urgent Finding Coordinates

    Please help me!
    Three points have coordinates A(2,5), B(10,9) and C(6,2). Line L1 passes through A and B. Line L2 passes through C and is perpendicular to L1.
    Find the coordinates of the point of intersection of L1 and L2? With working.
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  2. #2
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    The slope of AB = L1 is \frac{9-5}{10-2} = \frac{4}{8} = \frac{1}{2}. So the slope of the line through C (L2) will have opposite reciprocal slope, which is -2. Now use point-slope form ( y - y_0 = m(x - x_0)) to find the equations for both lines and then solve the system of equations given by the lines.
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  3. #3
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    Quote Originally Posted by kaley015 View Post
    Please help me!
    Three points have coordinates A(2,5), B(10,9) and C(6,2). Line L1 passes through A and B. Line L2 passes through C and is perpendicular to L1.
    Find the coordinates of the point of intersection of L1 and L2? With working.
    First, find the slope of the L1. Then define the equation.

    m=\frac{y_2-y_1}{x_2-x_1}=\frac{4}{8}=\frac{1}{2}

    Use y=mx+b with (2, 5) and m = 1/2

    y=mx+b

    5=\frac{1}{2}(2)+b

    5=1+b

    4=b

    Equation of L1 = \boxed{y=\frac{1}{2}x+4}

    Now use the negative reciprocal of the slope of L1 for your perpendicular.

    That would be -2. Use point C(6,2) and define the equation of your perpendicular as above.

    Use y=mx+b, m = -2, passing through C(6, 2)

    2=-2(6)+b

    2=-12+b

    14=b

    Equation of L2 = \boxed{y=-2x+14}

    Now, you can solve the system of those two linear equations and find where they intersect. Have fun.
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