# 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.

## 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