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# Algebra help!

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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

Apr 7, 2019