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.

JohnyGotchaApples Apr 7, 2019

#1**0 **

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

CPhill Apr 7, 2019