Results 1 to 4 of 4

Math Help - Find the end point

  1. #1
    Junior Member
    Joined
    Jul 2009
    Posts
    35

    Find the end point

    Hello guys, kindly help me in this problem. Thank you ^^

    The segment connecting (3,0) and (4,-1) is extended each way a distance (7/4) each own length. Find endpoint.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,413
    Thanks
    1853
    Quote Originally Posted by jasonlewiz View Post
    Hello guys, kindly help me in this problem. Thank you ^^

    The segment connecting (3,0) and (4,-1) is extended each way a distance (7/4) each own length. Find endpoint.
    The segment from (3, 0) to (4, -1) has "x range" 4- 2= 1 and "y range" -1- 0= -1: that is, to go from (3, 0) to (4, -1) you go to the right 1 and down 1. The "slope" is -1/1= -1. If you extend that line past (4, -1) you have to keep that same slope so you extend to the right some distance x and down that same distance: y= -x. Of course the distance is given by \sqrt{x^2+ y^2}= 7/4 and, since y= -x, that is \sqrt{x^2+ x^2}= \sqrt{2}x= 7/4. Add x= 7/(4\sqrt{2})= 7\sqrt{2}/8 to 4 and subtract it from 1 to get the (x,y) coordinates of the endpoint in that direction. Go the other way, past (3,0) to get the other endpoint.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello jasonlewiz
    Quote Originally Posted by jasonlewiz View Post
    Hello guys, kindly help me in this problem. Thank you ^^

    The segment connecting (3,0) and (4,-1) is extended each way a distance (7/4) each own length. Find endpoint.
    I assume that you want the coordinates of both end points.

    Draw a careful diagram showing these two points on a squared grid. Draw the line segment that joins them and extend it in each direction by \tfrac74=1\tfrac34 of its own length. So at the left-hand end that's 1\tfrac34 to the left and 1\tfrac34 units up; at the right-hand end that's 1\tfrac34 units to the right and 1\tfrac34 units down. If you draw this with care, you should see immediately what the coordinates are.

    The left-hand end point has x-coordinate 3 - 1\tfrac34=1\tfrac14; and y-coordinate 1\tfrac34.

    The right-hand end has x-coordinate 4 + 1\tfrac34 = 5\tfrac34; and y-coordinate -1-1\tfrac34=-2\tfrac34.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1
    Quote Originally Posted by jasonlewiz View Post
    The segment connecting (3,0) and (4,-1) is extended each way a distance (7/4) each own length. Find endpoint.
    This may be overkill, but here is a third way.
    The line determined by those two points can be written as \left\langle {3 + t, - t} \right\rangle ,\,t \in \mathbb{R}.
    If t=0 we get (3,0) and t=1 gives (4,-1).

    To get the two required points let t=\frac{-7}{4}~\&~t=\frac{11}{4}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 6th 2011, 07:44 AM
  2. Singular point: How can I numerically find the point of fracture?
    Posted in the Advanced Applied Math Forum
    Replies: 5
    Last Post: January 4th 2011, 03:30 AM
  3. Replies: 9
    Last Post: July 20th 2010, 09:00 AM
  4. Replies: 1
    Last Post: April 28th 2010, 08:59 PM
  5. Find the point on the line, closest to a point
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 14th 2009, 06:41 PM

Search Tags


/mathhelpforum @mathhelpforum