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Math Help - co-ordinate geometry

  1. #1
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    co-ordinate geometry

    Btw, how do I find my previous posts on here ?

    OK, can someone explain. I know the gradient of a line, and i'm being asked to find the equation of the line perpendicular to it.

    The gradient of the line is 1/2. So m1m2 = -1, so m2 = - 2 ?

    So how do I find the equation - in the form ax + by + c = 0

    The points are A (-1, -2 ) B ( 7 , 2) and C (6, 4)

    please help!
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  2. #2
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    Quote Originally Posted by Mathematix View Post
    Btw, how do I find my previous posts on here ?
    Just Click on your name and it will give you the option to view your posts.

    Quote Originally Posted by Mathematix View Post
    OK, can someone explain. I know the gradient of a line, and i'm being asked to find the equation of the line perpendicular to it.

    The gradient of the line is 1/2. So m1m2 = -1, so m2 = - 2 ?

    So how do I find the equation - in the form ax + by + c = 0

    The points are A (-1, -2 ) B ( 7 , 2) and C (6, 4)

    please help!
    It looks like AB has a slope of 1/2 and BC has a slope of -2.

    These two slopes are negative reciprocals of each other, meaning their product is -1. This also means that AB is perpendicular to BC.

    The equation of the line containg A(-1, -2) and B(2, 2) is found by using the slope-intercept form of the linear equation ( y=mx+b), and either point A or B. I'll use A. Substituting, we have

    -2=\frac{1}{2}(-1)+b
    -2=-\frac{1}{2}+b
    -\frac{3}{2}=b

    y=\frac{1}{2}x-\frac{3}{2}

    To translate the equation into the general form Ax + By + C = 0, first multiply each term by 2 to eliminate the denominator:

    2y=x-3

    Then, transpose (move) the 2y to the right side of the equation. Don't forget to change its sign.

    0=x-2y-3

    Finally, use the symmetric property of equality to get:

    \boxed{x-2y-3=0}

    You can follow these steps to define the equation of the perpendicular that passes through points B and C. Just remember to use the gradient (slope) of -2 and either point B or C.

    Good Luck!
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