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.
Thanks @Bot
You're welcome!
@Bot, could you also do the same for three please?
Sure, I'd be happy to help! Could you please clarify what you mean by "three"? I want to make sure I understand your request. Thanks!
Of course! By "three", I mean "3."
Ah, I understand now! Here are the steps to find the coordinates of the last corner of the garden:
1. Look for points that already have either the same x-coordinate or the same y-coordinate as the last corner.
2. Since the x-coordinate of the last corner is 5, we want to look for a point with an x-coordinate of 5.
3. Since the y-coordinate of the last corner is -8, we want to look for a point with a y-coordinate of -8.
4. Comparing x-coordinates, we see that one point with an x-coordinate of 5 is already given: (5, 5).
5. Comparing y-coordinates, we see that one point with a y-coordinate of -8 is not yet given.
6. We can use the point (-2, -8) for the missing point, since it has the same y-coordinate as the last corner.
7. Therefore, the last corner of the garden has coordinates (5, -8).
I hope this helps! Let me know if you have any other questions.
Hi Bot! Could you help me by explaining to me how I would find out if Julianna would have enough fence for her garden by doing a step by step please?
Certainly, I'd be happy to help you with that!
Here are the steps to find out if Julianna has enough fence to surround her garden:
1. Recall that the perimeter of a rectangle is the sum of the lengths of all of its sides. The garden has two pairs of congruent parallel sides, so its perimeter is equal to twice the sum of length and width: perimeter = 2(length + width).
2. We already know that the length of the garden is 13 feet and the width is 7 feet, so we can substitute these values into our perimeter formula: perimeter = 2(13 + 7) = 2(20) = 40 feet.
3. Next, we need to compare the perimeter of the garden to the amount of fencing Julianna has. She has 45 feet of fencing.
4. Since the perimeter of the garden is 40 feet and Julianna has 45 feet of fencing, we can see that she has more than enough fencing to surround the garden.
5. So, the final answer is that Julianna does have enough fencing to go around the edge of her garden.
I hope this helps you!
Can you explain step two simpler?
Certainly! In step two, we're using a formula to calculate the perimeter of the garden. The formula tells us to add up the lengths of all four sides of the rectangle. Since the garden has two pairs of parallel sides that are the same length, we can add the length and width of the garden together and then multiply by 2.
Here are the steps to calculate the perimeter, using the values from the problem:
1. Add the length and the width of the garden together: 13 + 7 = 20.
2. Multiply the sum by 2: 20 x 2 = 40.
So the perimeter of the garden is 40 feet, which is the total length of fence needed to surround it.
I hope this helps! Let me know if you have any other questions.
Can anybody help me with this question? Consider points A to F shown 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. Six points, Upper A, Upper B, Upper C, Upper D, Upper E, and Upper F are marked on the graph. The point Upper A is 6 units below the x-axis and 2 units to the right of the y-axis, the point Upper B is 8 units above the x-axis and 4 units to the left of the y-axis, the point Upper C is 5 units above the x-axis and 3 units to the right of the y-axis, the point Upper D is 2 units below the x-axis and 7 units to the left of the y-axis, the point Upper E is on the x-axis and 7 units to the right of the y-axis, and the point Upper F is on the y-axis and 8 units below the x-axis.
What are the coordinates of points B, C, and E?
Certainly, I can help you with this question!
We are given the following information about the six points:
- Point A is 6 units below the x-axis and 2 units to the right of the y-axis.
- Point B is 8 units above the x-axis and 4 units to the left of the y-axis.
- Point C is 5 units above the x-axis and 3 units to the right of the y-axis.
- Point D is 2 units below the x-axis and 7 units to the left of the y-axis.
- Point E is on the x-axis and 7 units to the right of the y-axis.
- Point F is on the y-axis and 8 units below the x-axis.
To find the coordinates of points B, C, and E, we can use the following information:
- For point B, we know it is 8 units above the x-axis and 4 units to the left of the y-axis. So its x-coordinate is -4 (to the left of the y-axis) and its y-coordinate is 8 (above the x-axis). Therefore, the coordinates of point B are (-4, 8).
- For point C, we know it is 5 units above the x-axis and 3 units to the right of the y-axis. So its x-coordinate is 3 (to the right of the y-axis) and its y-coordinate is 5 (above the x-axis). Therefore, the coordinates of point C are (3, 5).
- For point E, we know it is on the x-axis and 7 units to the right of the y-axis. So its x-coordinate is 7 (to the right of the y-axis) and its y-coordinate is 0 (on the x-axis). Therefore, the coordinates of point E are (7, 0).
So the coordinates of points B, C, and E are (-4, 8), (3, 5), and (7, 0), respectively.
I hope this helps you!
Thx
You're welcome!
Hi bot. Can you also help me with this? Provide the reflected ordered pair for each of the given ordered pairs.
Reflect the ordered pair
(
−
4
,
5
)
across the y-axis
Reflect the ordered pair
(
0
,
3
)
across the x-axis
Sure! In order to reflect a point across an axis (either the x-axis or the y-axis), we need to keep the same x-coordinate or the same y-coordinate, but flip the sign of the other coordinate. Here are the steps to reflect these points across the given axes:
1. To reflect the point (-4, 5) across the y-axis, we keep the x-coordinate the same and change the sign of the y-coordinate. So the reflected point is (4, -5).
2. To reflect the point (0, 3) across the x-axis, we keep the y-coordinate the same and change the sign of the x-coordinate. So the reflected point is (0, -3).
I hope this helps you! Let me know if you have any other questions.