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GEOMETRY QUESTION 1

  • 02-05-2012 8:40am
    #1
    JOANODEA
    Closed Accounts Posts: 9 ✭


    Help needed please!

    The point(1,3) lies on the line L1 while the point (4,5) lies on the line L2 making an angle of 45 degrees with L1. Find two possible equations of L1.


Comments

  • #2
    ray giraffe
    Registered Users, Registered Users 2 Posts: 338 ✭✭ray giraffe


    There isn't enough information to solve! Perhaps you forgot to write down some part of the question?


  • #3
    hivizman
    Registered Users, Registered Users 2 Posts: 1,163 ✭✭✭hivizman


    Actually, if all that is required are two possible lines, then a solution is given by the vertical line x = 1 and the horizontal line y = 3. Then taking the line L2 as y = 9 - x, this passes through the point (4,5), and intersects x = 1 at (1,8) and y = 3 at (6,3). The triangle made by the three points (1,3), (1,8) and (6,3) is a right-angled triangle with two sides (the two L1 lines) of equal length (5 units), so the angles between L2 and the two L1 lines are 45 degrees as required.

    If the question is seeking a unique pair of lines for L1, then more information is needed.


  • #4
    equivariant
    Registered Users, Registered Users 2 Posts: 966 ✭✭✭equivariant


    JOANODEA wrote: »
    Help needed please!

    The point(1,3) lies on the line L1 while the point (4,5) lies on the line L2 making an angle of 45 degrees with L1. Find two possible equations of L1.

    If this statement is accurate then L1 can be any line at all that passes through (1,3). Probably some condition missing from OP


  • #5
    gra26
    Registered Users, Registered Users 2 Posts: 197 ✭✭gra26


    Hivizman is correct. I remember doing a very similar one recently with some students and it's not asking for unique lines, so there's an infinite number of possibilities. It stumped me for a while until I realized


  • #6
    bnt
    Registered Users, Registered Users 2 Posts: 13,077 ✭✭✭✭bnt


    Since the question is asking only for the equation of a line L1 through (3,1), there must be something missing, since you could start with any line through (3,1). You could then find a line L2 through (5,4) that meets L1 at 45 degrees, but you aren't being asked for that. Does L1 or L2 pass through the origin, or something like that?

    You are the type of what the age is searching for, and what it is afraid it has found. I am so glad that you have never done anything, never carved a statue, or painted a picture, or produced anything outside of yourself! Life has been your art. You have set yourself to music. Your days are your sonnets.

    ―Oscar Wilde predicting Social Media, in The Picture of Dorian Gray



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  • #7
    Anonymo
    Registered Users, Registered Users 2 Posts: 151 ✭✭Anonymo


    JOANODEA wrote: »
    Help needed please!

    The point(1,3) lies on the line L1 while the point (4,5) lies on the line L2 making an angle of 45 degrees with L1. Find two possible equations of L1.

    There was an error in the question for this one.
    The intended question (and solution) are here
    http://www.educate.ie/files/abq/HigherleveMathspapersol.pdf


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