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Analytic Geometry World Problem

  1. Mar 20, 2012 #1

    S.R

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    1. The problem statement, all variables and given/known data
    Points S and T lie on the line 2x+y=3. If the length ST is 13 units, and the coordinates of S are (2, -1), determine all possible coordinate pairs for T, correct to two decimal places.

    For simplicity, determine the coordinates for T, relative to S from the left.


    2. Relevant equations
    a^2=b^2+c^2 (in this problem, the distance formula.)


    3. The attempt at a solution
    I used a system of equations:

    y=-2x+3

    (2-x)^2+(-1-y)^2=13^2

    This system is quite tedious. I used WolframAlpha to compute the solutions, however, they did not match the answer in my textbook.

    Is this approach correct?
     
    Last edited: Mar 20, 2012
  2. jcsd
  3. Mar 20, 2012 #2
    Think of a circle with a diameter of 13 at point (2,-1). It helps if you actually draw this. To get to a coordinate or point on the arc you would...
     
  4. Mar 20, 2012 #3

    HallsofIvy

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    Staff Emeritus
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    Kingstrick, that is exactly what he is doing. S.R., yes, that is a valid method. of course, you can replace the y in the circle equation by -2x+ 3 so that it becomes
    [tex](2- x)^2+ (-1-(-2x+3))^2= (2- x)^2+ (2x- 4)^2= 13. Multiplying that out will give you a quadratic equation which will have 2 solutions because, of course, this line is a diameter of the circle and so crosses it twice.
     
  5. Mar 20, 2012 #4

    S.R

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    Thanks HallsofIvy!
     
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