Results 1 to 2 of 2

Math Help - 2D plane intersection point

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    1

    2D plane intersection point

    Hello all,

    i need help with the following question:


    Given a 2d plane which has 4 distinct points, C, D, A, B. Points A and B define an infinite line. At time t=0 a player starts moving at a constant velocity from point C to point D, where he arrives at t=1. Determine, if the player hits the wall. If he does, find the corresponding time and position.


    I started this problem by taking an infinite length line AB and from the given data , the distance of CD is V(v=velocity from C to D). But I am unable to understand about how to find the intersection of the two lines. I started by trying to find if C and lie on either side of AB or on AB but could not proceed much with this. Can someone plz help me out with problem.


    Thanx a lot ,
    Aarav
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,325
    Thanks
    1296
    Quote Originally Posted by arnav.akash9 View Post
    Hello all,

    i need help with the following question:


    Given a 2d plane which has 4 distinct points, C, D, A, B. Points A and B define an infinite line. At time t=0 a player starts moving at a constant velocity from point C to point D, where he arrives at t=1. Determine, if the player hits the wall. If he does, find the corresponding time and position.
    Are we to assume that the line AB is the "wall" you mention?

    Given points (x_1, y_1) and (x_2, y_2), the equation of the line through them is (x_2- x_1)(y- y_1)= (y_2- y_1)(x- x_1) or  y= \frac{y_2- y_1}{x_2- x_1)(x- x_1)+ y_1.

    Find the equations of the two lines in that form and set the "y"s equal:
    The line through A and B is y= \frac{y_B-y_A}{x_B-x_A}(x- x_A)+ y_A and the line through C and D is y= \frac{y_D-y_C}{x_D-x_C)(x- xC)+ y_C. Setting those two "y"s equal gives the linear equation \frac{y_B-y_A}{x_B-x_A}(x- x_A)+ y_A= \frac{y_D-y_C}{x_D-x_C)(x- xC)+ y_C which you can solve for x.

    Now, go back and write line CD in terms of t. Since the line passes through C at t= 0 and D at t= 1, it can be written as x= (x_D- x_C)t+ x_C, y= (y_D-y_C)t+ y_C.

    Put the value you got for x or y into one of those equations and solve for t.

    I started this problem by taking an infinite length line AB and from the given data , the distance of CD is V(v=velocity from C to D). But I am unable to understand about how to find the intersection of the two lines. I started by trying to find if C and lie on either side of AB or on AB but could not proceed much with this. Can someone plz help me out with problem.


    Thanx a lot ,
    Aarav
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: October 4th 2011, 10:59 AM
  2. [SOLVED] Position vector of point of intersection of line and plane
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: July 1st 2010, 03:14 AM
  3. Intersection point of a line and a plane
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 20th 2010, 03:28 PM
  4. Replies: 0
    Last Post: November 19th 2008, 06:04 AM
  5. Point of intersection of a line with plane
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 2nd 2008, 08:16 AM

Search Tags


/mathhelpforum @mathhelpforum