# Real life coordinate geometry problem

To conduct a sport activities, in a rectangular shaped school ground $ABCD$, lines have been drawn with chalk powder at a distance of $1$ m each. $100$ flower pots have been placed at a distance of $1$ m height from each other along AD, as shown in figure. Child A runs $\frac{1}{4}$th the distance AD on the 2nd line and post a green flag. Child B runs $\frac{1}{5}$th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Child C has to post a blue flag exactly halfway between the line segment joining the two flags, where should Child C post the flag?

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why is this tagged algebraic-geometry? – andybenji Dec 25 '12 at 17:41

Ok. Here is how I tried to solve it. I am assuming that the first flower pot is located 1m higher than point A. Then we can interpret the location of each flower pot as the point (0,n). Where n is the number of flower pot (counting from the bottom upwards). The vertical lines can also be interpreted in the same way. That is each line occupies the points (l,r) where l is the number of the line (from left to right) and r occupies all the reals (so the line actually exists for all points up and down). Ok Child a runs 1/4 of line AD. I am assuming that the 100th flower pot lies on point D. Then the distance AD=100. Therefore child a ran 25 meters and is currently on point (2,25) analogously child b ended up on point (8,20). So now all we have to do is find the distance between points (2,25) and (8,20).

To do this we realize that (2,25),(8,20),(2,20) make a right triangle with the lengths of the legs being 5,6. using the fact that the sum of the squares of the legs is equal to the square of the hypotenuse we get that the square of the hypotenuse is 25+36=61. Therefore the length you are looking for is $\sqrt 61$.

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You should specify that the distance between the radii of the pots is 1. Not between the pots themselves. – Carry on Smiling Dec 25 '12 at 17:41

1 approach:

Just draw it on a piece of paper:

I got for the distance green flag to red flag $30m$.

The blue flag should be put on the 5th line and in the Distance of $AD= 11/50$

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I don't think so. – Ross Millikan Dec 25 '12 at 16:02

Hint: If the children start along AB, the green flag is at (2,25) and the red at (8,20) The distance comes from Pythagoras, the midpoint from averaging.

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