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Thread: Find the end point

  1. #1
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    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.
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    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 $\displaystyle \sqrt{x^2+ y^2}= 7/4$ and, since y= -x, that is $\displaystyle \sqrt{x^2+ x^2}= \sqrt{2}x= 7/4$. Add $\displaystyle x= 7/(4\sqrt{2})= 7\sqrt{2}/8$ 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.
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  3. #3
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    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 $\displaystyle \tfrac74=1\tfrac34$ of its own length. So at the left-hand end that's $\displaystyle 1\tfrac34$ to the left and $\displaystyle 1\tfrac34$ units up; at the right-hand end that's $\displaystyle 1\tfrac34$ units to the right and $\displaystyle 1\tfrac34$ units down. If you draw this with care, you should see immediately what the coordinates are.

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

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

    Grandad
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    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 $\displaystyle \left\langle {3 + t, - t} \right\rangle ,\,t \in \mathbb{R}$.
    If $\displaystyle t=0$ we get $\displaystyle (3,0)$ and $\displaystyle t=1$ gives $\displaystyle (4,-1)$.

    To get the two required points let $\displaystyle t=\frac{-7}{4}~\&~t=\frac{11}{4}$.
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