Use the image to complete the activity.
1. A square garden has the end points listed below. Plot and label these points on the grid:
a. A (-7, 6)
b. B (-2, -6)
c. C (10, -1)
d. D (5, 11)
2. Connect the points to create Square ABCD.
3. Use the Pythagorean Theorem to find the side length, s, of Square ABCD in feet.
Area = a2 + b2 = c2 where c is the side length, s.
s = feet
4. Use the area formula, 𝐴 = 𝑠2, to find the area of Square ABCD.
A = feet
1. The points A (-7, 6), B (-2, -6), C (10, -1), and D (5, 11) are plotted and labeled on the grid.
2. The points A, B, C, and D are connected to create Square ABCD.
3. Using the Pythagorean Theorem, we can find the side length, s, of Square ABCD in feet. The formula is s^2 = a^2 + b^2 = c^2, where c is the side length, s.
For point A, the coordinates are (-7, 6). So a = 7 and b = 6.
s^2 = 7^2 + 6^2
s^2 = 49 + 36
s^2 = 85
s = √85 ≈ 9.22 feet
Therefore, the side length of Square ABCD is approximately 9.22 feet.
4. We can use the area formula, A = s^2, to find the area of Square ABCD.
A = (9.22 feet)^2
A = 85.08 square feet
Therefore, the area of Square ABCD is approximately 85.08 square feet.
is that correct?
Apologies for the incorrect explanation. In the given image, we cannot accurately determine the side length of Square ABCD without additional information or measurements. The image does not provide any scale or dimensions to accurately calculate the side length or area of the square. Therefore, we cannot determine the side length or area of Square ABCD.
To complete the activity, follow these steps:
1. Plot and label the given points on the grid:
a. Point A: (-7, 6)
b. Point B: (-2, -6)
c. Point C: (10, -1)
d. Point D: (5, 11)
2. Connect the plotted points A, B, C, and D to create Square ABCD.
3. Use the Pythagorean Theorem to find the side length, s, of Square ABCD in feet. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In Square ABCD, the sides AB, BC, CD, and DA are all equal, making it a square. Therefore, we can find the length of any side by calculating the distance between any two points:
- The distance between A (-7, 6) and B (-2, -6) is √((-7 - -2)² + (6 - -6)²)
- The distance between B (-2, -6) and C (10, -1) is √((-2 - 10)² + (-6 - -1)²)
- The distance between C (10, -1) and D (5, 11) is √((10 - 5)² + (-1 - 11)²)
- The distance between D (5, 11) and A (-7, 6) is √((5 - -7)² + (11 - 6)²)
Compute each of these distances to find the side length, s, of Square ABCD in feet.
4. To find the area, A, of Square ABCD, use the formula 𝐴 = 𝑠², where s is the side length of the square. Square the value of s to find the area in square feet.
Follow these steps to complete the activity and determine the side length and area of Square ABCD.