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).
Find the coordinates of the last corner of the garden.
Determine the length and width of the garden using absolute value.
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.
1. To find the coordinates of the last corner, let's look at the points given. We have the points (-2, -8), (-2, 5), and (5, 5). To maintain a rectangle, we should choose a point that is horizontally across from (-2, -8), and vertically across from (5, 5). So the point we need has an x-coordinate of 5, and a y-coordinate of -8. This tells us the last corner is at (5, -8).
2. To determine the length and the width of the garden, we can measure the horizontal and vertical distances between the points. The width of the garden would be the distance between the x-coordinates of (-2, -8) and (5, -8), so we calculate the absolute value of |-2 - 5| = |-7| = 7 feet. The length of the garden would be the vertical distance between the y-coordinates of (-2, -8) and (-2, 5), so we calculate the absolute value of |-8 - 5| = |-13| = 13 feet.
3. To determine if Julianna has enough fence for the garden, we need to calculate the perimeter of the garden. Since the garden is rectangular, the perimeter is simply 2 * (length + width) = 2 * (13 + 7) = 2 * 20 = 40 feet. Since Julianna has 45 feet of fencing, we can see that she has more than enough to fence the garden.
@Bot, could you explain step 2 simpler please?
Certainly! To find the width of the garden, we need to subtract the x-coordinate of the left corner (-2) from the x-coordinate of the right corner (5), and take the absolute value of the result: |5 - (-2)| = |7| = 7 feet. Similarly, to find the length of the garden, we need to subtract the y-coordinate of the bottom corner (-8) from the y-coordinate of the top corner (5), and take the absolute value of the result: |5 - (-8)| = |13| = 13 feet.
Could you maybe make that into steps please? Thank you!
Yes, of course! Here are the steps to find the width and length of the garden:
To find the width:
1. Subtract the x-coordinate of the left corner from the x-coordinate of the right corner. (In this case, 5 - (-2) = 7.)
2. Take the absolute value of the result. (In this case, the absolute value of 7 is 7.)
So the width of the garden is 7 feet.
To find the length:
1. Subtract the y-coordinate of the bottom corner from the y-coordinate of the top corner. (In this case, 5 - (-8) = 13.)
2. Take the absolute value of the result. (In this case, the absolute value of 13 is 13.)
So the length of the garden is 13 feet.