1. What shape should Kylee use to draw the swimming pool on the diagram? 2.If Kylee wanted to put the swimming pool directly between the flower beds, at what point would the center of the swimming pool be? 3.Use the point you identified in Part 1 to write an equation that will draw the swimming pool on the diagram so that it is directly between the flower beds. 4.Can Kylee place the swimming pool directly between the flower beds? Use the equation you wrote in Part 3 prove or disprove that the swimming pool will touch one of the flower beds. (Hint: Plug in points that are on a flower bed to check if they are also on the circle.) 5.Where can Kylee put the pool? Write an equation that will draw the pool on the diagram so that it does not touch anything.

1) A rectangular shape

2) Point  (30, 50)

3) (x - 30)² + (y - 50)² = 10²

4) Yes, the swimming pool will touch the flower beds

5) Point (45, 25)

Step-by-step explanation:

1) Given the number of shapes that are rectangles (4) and the number of circular shapes (1) to conserve more space Kylee should drw the swimming pool with a rectangular shape

2)  So as to avoid touching the flowerbeds which are 20 feet apart, the center of the swimming pool will be moved slightly up to (30, 50)

3) The equation that will draw the swimming pool is the equation of a circle, given as follows

(x - h)² + (y - k)² = r²

Where (h, k) is the coordinate of the center of the circle, and r is the radius of the circle,

Given that the diameter, D, of the circle = 20 feet, the radius, r = D/2 = 20/2 = 10 feet

The equation of the circle is therefore;

(x - 30)² + (y - 50)² = 10²

4) The coordinates of the center of the flower bed is (30, 45) which gives

(x - 30)² + (y - 45)² = 10²

Where the coordinates of the side of the flower pot is (20, 45), we have;

(20 - 30)² + (45 - 45)² = 10²

(-10)² = 10² = r²

Hence, point (20, 45) is on the circle

The other flower bed side has coordinates (40, 45) which gives

(40 - 30)² + (45 - 45)² = 10²

10² = r² = 10²

Point (40, 45) is also on the circle

Therefore, the swimming pool will touch the flower beds

5) At point (45, 25), we have;

(x - 45)² + (y - 25)² = 10²

The closest point is the patio with coordinates (40, 15) which gives;

(40 - 45)² + (15 - 25)² = 10² = 100

(-5)² + (-10)² = 125 > 100

Therefore, point (40, 15), is not on the circle.