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Math Help - Equation of the straight line

  1. #1
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    Equation of the straight line

    The coordinates of E,F and H of an equilateral are (3,3),(0,-1)and (6,2) respectively. FH is perpendicular to EG whereas the straight line FG is parallel to x-axis.Find

    a)the equation of straight line EG

    b)the coordinates of point G

    c)the equation of locus R such that the distance of R from point E and F are equal.
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  2. #2
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    The coordinates of and of an equilateral are and respectively.
    EFG is not an equilateral triangle.
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    The coordinates of and of an equilateral are and respectively.
    EFG is not an equilateral triangle.
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  4. #4
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    Quote Originally Posted by lindros View Post
    The coordinates of E,F and H of an equilateral are (3,3),(0,-1)and (6,2) respectively. FH is perpendicular to EG whereas the straight line FG is parallel to x-axis.Find

    a)the equation of straight line EG
    Since EG is perpendicular to FH, which has slope 1/2, EG has slope -2. That means that EG has equation y= -2(x- 3)+ 3.

    b)the coordinates of point G
    Since FG is parallel to the x-axis, G must have the same y coordinate as F: -1. Solve -1= -2(x- 3)+ 3 to find the x coordinate.

    c)the equation of locus R such that the distance of R from point E and F are equal.
    This is the straight line perpendicular to EF and passing through its midpoint. EF has slope (3-(-1))/(3- 0)= 4/3 so this line has slope -3/4. The midpoint of EF is ((3+(-1))/2, (3+ 0)/2).
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