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anonymous

  • one year ago

A gardner wants the rosebushes in her garden to be water by a rotating water sprinkler. The gardner draws a diagram of the garden using a grid in which each unit represents 1 ft. The rosebushed are at (1,3), (5,11), and (11,4). She wants to position the sprinkler at a point equidistant from each rosebush. Where should the gardner place the sprinkler? What equation describes the boundary of the circular region that he sprinkler will cover?

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  1. anonymous
    • one year ago
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    I believe you use a midpoint formula being m=(x1+x2/2, y1+y2/2) but that didnt really work so i need help with what formula to use i already drew it on graph paper.

  2. anonymous
    • one year ago
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    i know it's coordinate geometry

  3. anonymous
    • one year ago
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    I think you might need to set up a system of equations using the distance formula. Let d be the distance between the sprinkler and the rosebushes, and (x, y) be the coordinates of the sprinkler. Then the three equations for the system are \[d=\sqrt{(x-1)^2+(y-3)^2}\] \[d=\sqrt{(x-5)^2+(y-11)^2}\] \[d=\sqrt{(x-11)^2+(y-4)^2}\]

  4. anonymous
    • one year ago
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    Set any two of the equations equal to each other to eliminate d.

  5. anonymous
    • one year ago
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    Or you could draw a triangle between the three points and find the intersection perpendicular bisectors

  6. anonymous
    • one year ago
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    it's impossible so i gave up and gave it to my teacher but thank you.

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