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Math Help - Writing equation of locus

  1. #1
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    Writing equation of locus

    A point P(x,y) moves such that it is equidistant from the points (-4,7) and (3,-2). What is the equation that represent this locus?

    I don't know how to do this question. Please help.

    Thanks.
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  2. #2
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    Quote Originally Posted by shenton View Post
    A point P(x,y) moves such that it is equidistant from the points (-4,7) and (3,-2). What is the equation that represent this locus?

    I don't know how to do this question. Please help.

    Thanks.

    Hello, shenton,

    the point P moves on the perpendicular bisector of the straight line from A(-4, 7) and B(3, -2).

    1. Calculate the coordinates of the midpoint M of AB: M((-4+3)/2, (7-2)/2)
    2. Calculate the slope of AB: (7-(-2))/(-4-3) = -9/7
    3. The perpendicular direction is therefore: m = 7/9

    Now you have a point and the slope of the line you are looking for. Use the point-slope-formula of a line:

    (y - 5/2)/(x - (-1/2)) = 7/9 . Multiply by the denominator:

    y - 5/2 = 7/9x + 7/18 Finally you get:

    y = 7/9x + 26/9

    EB




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  3. #3
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    Hello, shenton,

    I've attached a diagram of all the results of my calculations.

    If you choose a point on the perpendicular bisector you'll see that it has the same distance to A and to B.

    EB

    Attached Thumbnails Attached Thumbnails Writing equation of locus-locus-p-.gif  
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  4. #4
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    Hello, shenton!

    A point P(x,y) moves such that it is equidistant from the points A(-4,7) and B(3,-2).
    What is the equation that represent this locus?
    Hey, how about using the Distance Formula?

    . . . . . . . - . - . . . . . ._______________
    The distance PA is: . √(x + 4) + (y - 7)
    . . . . . . . - . - . . . . . ._______________
    The distance PB is: . √(x - 3) + (y + 2)

    . . . . . . . . . . . . . _______________ . . - . ._______________
    Since PA = PB: . √(x + 4) + (y - 7) . = . √(x - 3) + (y + 2)


    Square both sides: . (x + 4) + (y - 7) . = . (x - 3) + (y + 2)

    Expand: . x + 8x + 16 + y - 14y + 49 . = . x - 6x + 9 + y + 4y + 4

    . . which simplifies to: . 14x - 18y + 52 .= .0 . . y .= .(7/9)x + 26/9

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