Geometry

posted by .

A gardener wants the three rosebushes in her garden to be watered by a rotating water sprinkler. The gardener draws a diagram of the garden using a grid in which each unit represents 1 ft. The rosebushes 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 gardener place the sprinkler? What equation describes the boundary of the circular region that the sprinkler will cover?

  • Geometry -

    the center of the circle will be at the intersection of the perpendicular bisectors of two of the line segments joining the points. If we label the points
    A:(1,3)
    B:(5,11)
    C:(11,4)
    then we have
    AB: midpoint=(3,7) slope=2
    BC: midpoint=(8,15/2) slope=-7/6
    CA: midpoint=(6,7/2) slope=1/10
    so, the equations of the perpendicular bisectors are
    AB: y = 1/2 (17-x)
    AC: y = 3/14 (4x+3)
    CA: y = 1/2 (127-20x)

    These all intersect at (220/38,213/38)

    The radius of the circle is 5√1717/38

    (x-220/38)^2 + (y-213/38)^2 = 42925/1444 = 29.726

    Ouch! Hard to believe, but the math checks out.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Poem: Incident in a rose garden: By Donald Justice

    Could someone please check my answers to the poem thanks. 1. How does the gardener recongize Death?
  2. Algebra

    A gardener has 60 feet of fencing with which to enclose a garden adjacent to a long existing wall. The gardener will use the wall for one side and the available fencing for the remaining three sides. (a) If the sides perpendicular …
  3. math

    A gardener wants to create a rectangular garden with length of 8x - 4y ft. and width of 5x + 9y ft. What is an algebraic expression for the area of the garden?
  4. math

    a gardener is planning to make a rectangular garden with an area of 80ft^2.she has 12 yards of fencing to put around the perimeter of the garden.what should the dimension of the garden be ?
  5. Math

    A gardener is putting a fence along the edge of his garden. If he has 20 m of fence , what is the largest area he can enclose?
  6. Algebra 11

    The diagram shows the plan made by a landscape artist for a homeowner's 16-meter by a 16-meter backyard . The homeowner has requested that rosebushes, fountain, and garden bench be placed so that they are no more that 14 meters apart. …
  7. Algebra II

    The diagram shows the plan made by a landscape artist for a homeowner's 16-meter by a 16-meter backyard . The homeowner has requested that rosebushes, fountain, and garden bench be placed so that they are no more that 14 meters apart. …
  8. math

    a rotating sprinkler is placed in one corner of a rectangular garden 12cm by 8cm and rotates through an angle of 30°. Calculate the area of the garden not being watered
  9. cne

    A rectangular garden measures 3 feet by 15 feet. The gardener decides to extend the garden 1 foot in each of the four directions. What is the perimeter of the new garden in feet?
  10. math

    3) You are fencing a rectangular puppy kennel with 25 ft of fence. The side of the kennel against your house does not need a fence. This side is 9 ft long. Find the dimensions of the kennel. 4) A gardener is planning a rectangular …

More Similar Questions