Results 1 to 2 of 2

Math Help - [SOLVED] Analytic Geometry Q9

  1. #1
    Member looi76's Avatar
    Joined
    Jan 2008
    Posts
    185

    [SOLVED] Analytic Geometry Q9

    Question:
    A line passes through the points: A(1,1) & B(5,7). Find the coordinates of P if P is three times as far from A as from B.

    Attempt:
    I know that I can find the points of P using this formula: X = x_1 + r(x_2 - x_1) & Y = y_1 + r(x_2 - x_1), but how can I find r?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by looi76 View Post
    Question:
    A line passes through the points: A(1,1) & B(5,7). Find the coordinates of P if P is three times as far from A as from B.

    Attempt:
    I know that I can find the points of P using this formula: X = x_1 + r(x_2 - x_1) & Y = y_1 + r(x_2 - x_1), but how can I find r?
    There are two different points P. In my sketch one point is P_{red} and the other is P_{blue}.

    1. P_{red}: Use proportions:

    \dfrac{AP}{PB}=\dfrac31~\implies~\dfrac{AP}{AB-AP}=3

    Solve for AP. I've got AP=\underbrace{\frac34}_{\text{= r}} \cdot AB

    2. If you use the equation of the line:

    l:\left\{\begin{array}{l}x=1+r\cdot (5-1) \\ y=1+r \cdot (7-1)\end{array}\right.~\wedge r=\frac34~\implies~ \begin{array}{l}x=4 \\ y=\frac{11}2\end{array}

    3. I leave the calculation of the coordinates of P_{blue} to you. (For confirmation only: (7, 10))
    Attached Thumbnails Attached Thumbnails [SOLVED] Analytic Geometry Q9-zweipkte_auflinie.png  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] analytic geometry
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 10th 2011, 11:00 PM
  2. [SOLVED] Analytic Geometry doubt?
    Posted in the Geometry Forum
    Replies: 4
    Last Post: June 2nd 2009, 10:00 AM
  3. Analytic Geometry Q10
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: March 4th 2009, 04:05 AM
  4. Analytic Geometry Q6
    Posted in the Geometry Forum
    Replies: 3
    Last Post: January 31st 2009, 04:14 AM
  5. [SOLVED] rhombus analytic geometry
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: September 29th 2008, 12:26 AM

Search Tags


/mathhelpforum @mathhelpforum