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Tina the tourist goes on a trip. She starts at the origin and drives north (in the positive $y$ direction) for $10$ units. Then she turns east (the positive $x$ direction) and as she's turning her camera flies out the window and lands exactly at $(0,10)$. She then drives $9$ units east, turns and drives $8$ units north. She continues this pattern of turning and driving one unit less than after the previous turn, until stopping after driving $1$ unit east. She reaches for her camera only to find it missing! She activates the GPS homing device on her camera and drives back to it in a straight line. What is the equation of this line? Express your answer as $ax+by=c$, where $a$, $b$, and $c$ are integers, $a>0$, and $a$ is as small as possible.

 Apr 7, 2019
edited by JohnyGotchaApples  Apr 7, 2019
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If I understand this correctly, JGA.....we have these series of moves  from the origin

 

East = x       North = y

  0                 10

  9                  8

  7                  6

  5                  4

  3                  2

  1                  0

 

Adding both columns.....she ends up  at the point  ( 25, 30)

 

So...the slope of the line  joining this point to (0, 10)  is found as  [ 30 - 10 ] / [ 25 - 0 ]  = 20/25  = 4/5

 

And the equation of the line joining these two points is given by :

 

y = (4/5)(x - 0) + 10

 

y = (4/5)x + 10         we want this in standard form, so.......multiply through by 5

 

5y = 4x + 50         subtract 5y from both sides

 

4x - 5y  + 50  = 0

 

4x - 5y = -50

 

 

cool cool cool

 Apr 7, 2019

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