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Thread: Equation of the straight line

  1. #1
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    Equation of the straight line

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

    a)the equation of straight line $\displaystyle EG$

    b)the coordinates of point $\displaystyle G$

    c)the equation of locus $\displaystyle R$ such that the distance of $\displaystyle R$ from point $\displaystyle E$ and $\displaystyle F$ 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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  3. #3
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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 $\displaystyle E,F$ and $\displaystyle H$ of an equilateral are $\displaystyle (3,3),(0,-1)$and $\displaystyle (6,2)$ respectively.$\displaystyle FH$ is perpendicular to $\displaystyle EG$ whereas the straight line $\displaystyle FG$ is parallel to $\displaystyle x-axis$.Find

    a)the equation of straight line $\displaystyle EG$
    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 $\displaystyle G$
    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 $\displaystyle R$ such that the distance of $\displaystyle R$ from point $\displaystyle E$ and $\displaystyle F$ 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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