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.
A). Has the landscape artist met the homeowner's requirements? Explain and show work.
B)The homeowner has purchased a sundial to be placed midway between the fountain and the rosebushes. Determine the coordinates indicating where the sundial should be placed.
A) To determine if the landscape artist has met the homeowner's requirements, we need to compare the distances between the elements (rosebushes, fountain, and garden bench) in the plan. The homeowner requested that these elements be placed no more than 14 meters apart.
First, let's identify the positions of the elements in the diagram. Since the backyard is 16 meters by 16 meters, we can assume it forms a square. Let's label the corners of the square as A, B, C, and D.
If we consider the bottom-left corner of the backyard square (point A) as the origin (0, 0), we can determine the coordinates of the elements.
Let's assume the rosebushes are at point R (x coordinates, y coordinates), the fountain is at point F (x coordinates, y coordinates), and the garden bench is at point G (x coordinates, y coordinates).
To check if the requirements are met, we need to calculate the distances between each pair of elements and compare them to 14 meters.
For example, let's calculate the distance between the rosebushes and the fountain:
Distance = √((x_R - x_F)^2 + (y_R - y_F)^2)
If this distance is less than or equal to 14, then the requirement is met. Repeat the process for other pairs of elements to ensure all distances are less than or equal to 14 meters.
B) To determine the coordinates of the sundial, we need to find the midpoint between the fountain and the rosebushes.
First, calculate the coordinates of the midpoint using the following formula:
Midpoint x-coordinate = (x_R + x_F) / 2
Midpoint y-coordinate = (y_R + y_F) / 2
These calculated coordinates represent the midpoint between the fountain and the rosebushes. Place the sundial at these coordinates to meet the homeowner's requirement of being placed midway between the two elements.