Julianna is making a rectangular garden in her backyard. She has plotted three of the corners on the coordinate plane.
A graph is shown in the xy-plane. The values on the x-axis ranges from negative 8 to 8 in increments of 2 and the values on the y-axis ranges from negative 8 to 8 in increments of 2. Three points are marked on the graph whose coordinates are (negative 2, negative 8), (negative 2, 5), and (5, 5).
A. Find the coordinates of the last corner of the garden.
B. Determine the length and width of the garden using absolute value.
C. Julianna bought 45 feet of fencing to go around the edge of the garden. If each unit in the coordinate plane represents 1 foot, does Julianna have enough fencing for the garden? Be sure to explain your answer.
A. The three given coordinates of the rectangular garden are (-2, -8), (-2, 5), and (5, 5). We can find the last corner of the garden by comparing the x and y coordinates of the given points. Specifically, we can find the corner which has x-coordinate 5 and y-coordinate -8. Thus, the last corner of the garden has coordinates (5, -8).
B. To determine the length and width of the garden, we can find the distance between the x-coordinates and the y-coordinates of the corners of the garden:
Width = |(-2) - (5)| = |-7| = 7 feet
Length = |(-8) - (5)| = |-13| = 13 feet
So, the garden has a width of 7 feet and a length of 13 feet.
C. Let's find the perimeter of the garden:
Perimeter = 2(Length + Width) = 2(7 + 13) = 2(20) = 40 feet
Since Julianna bought 45 feet of fencing, she has enough fencing for the garden because the perimeter of the garden is 40 feet, which is less than 45 feet.
To find the coordinates of the last corner of the garden, we need to find the point that is not already given. Since the three points given are (-2, -8), (-2, 5), and (5, 5), we can observe that the last corner must have the same x-coordinate as the second point and the same y-coordinate as the third point. Thus, the coordinates of the last corner are (-2, 5).
To determine the length and width of the garden, we can use the absolute value of the differences in the x-coordinates and y-coordinates of the given points. The length of the garden can be found by taking the absolute value of the difference in the x-coordinates of the first and second points: |(-2) - (-2)| = 0. The width of the garden can be found by taking the absolute value of the difference in the y-coordinates of the second and third points: |5 - 5| = 0. Therefore, the length and width of the garden are both 0.
For part C, since the length and width of the garden are both 0, it means that there is no area enclosed by the garden and hence no need for any fencing. Therefore, Julianna has enough fencing for the garden because no fencing is required.