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.
I'm sorry, but as a language model AI, I cannot create graphics or visual representations. However, I can help you with the calculations and provide you with the steps to find the side length of the square.
To find the side length of the square ABCD using the Pythagorean Theorem, you need to calculate the distance between two neighboring points. Let's take points A (-7, 6) and B (-2, -6) as an example.
The distance formula is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
So, for points A and B, the distance is:
d = √((-2 - (-7))^2 + (-6 - 6)^2)
= √((5)^2 + (-12)^2)
= √(25 + 144)
= √(169)
= 13
Therefore, the side length of the square ABCD is 13 feet.
1. To plot and label the points on the grid, we will use the x-axis to represent the horizontal axis and the y-axis to represent the vertical axis.
a. Point A (-7, 6): Plot a point at -7 on the x-axis and at 6 on the y-axis.
b. Point B (-2, -6): Plot a point at -2 on the x-axis and at -6 on the y-axis.
c. Point C (10, -1): Plot a point at 10 on the x-axis and at -1 on the y-axis.
d. Point D (5, 11): Plot a point at 5 on the x-axis and at 11 on the y-axis.
2. To connect the points and create Square ABCD, draw lines between each consecutive pair of points. Connect point A to point B, point B to point C, point C to point D, and finally point D back to point A.
3. To find the side length of Square ABCD using the Pythagorean Theorem, we need to find the distance between two adjacent points. Let's find the distance between points A and B.
Using the Pythagorean Theorem:
Distance^2 = (Change in x)^2 + (Change in y)^2
Distance^2 = (-7 - (-2))^2 + (6 - (-6))^2
Distance^2 = (-7 + 2)^2 + (6 + 6)^2
Distance^2 = (-5)^2 + (12)^2
Distance^2 = 25 + 144
Distance^2 = 169
Taking the square root of both sides:
Distance = √169
Distance = 13
Therefore, the side length of Square ABCD is 13 feet.
To plot the points on a grid:
1. Draw a grid on a piece of paper, ensuring that the x-axis and y-axis intersect at the center.
2. Locate the point A (-7, 6) by counting 7 units to the left along the x-axis and 6 units up along the y-axis from the origin (center).
3. Place a labeled point at the location of A on the grid.
4. Repeat steps 2 and 3 for the remaining points B (-2, -6), C (10, -1), and D (5, 11).
To connect the points and create Square ABCD:
1. Use a straightedge or ruler to draw line segments connecting the points A, B, C, and D, in sequence.
2. Ensure that the lines are straight and intersect correctly to form a closed shape.
To find the side length, s, of Square ABCD using the Pythagorean Theorem:
1. Identify any two adjacent points (A and B, B and C, C and D, or D and A), and label them as the endpoints of a diagonal.
2. Use the coordinates of these points to determine the lengths of the horizontal and vertical sides of the square.
- For example, the horizontal side length h can be found by subtracting the x-coordinates: h = Bx - Ax.
- The vertical side length v can be found by subtracting the y-coordinates: v = By - Ay.
3. Apply the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c^2 = a^2 + b^2.
- In this case, the hypotenuse is the diagonal, and the other two sides are the horizontal and vertical side lengths of the square.
4. Square both the horizontal and vertical side lengths (h^2 and v^2), and add them together to get c^2: c^2 = h^2 + v^2.
5. Take the square root of c^2 to find the length of the diagonal (s): s = √(h^2 + v^2).
So, to find the side length of Square ABCD, you'll need to calculate the lengths of its sides using the given coordinates and then use the Pythagorean Theorem to find the diagonal, which will be the same as the side length.
Now, using that information, use the area formula, 𝐴𝐴 = 𝑠𝑠2, to find the area of Square ABCD.
A = ________feet
To find the area of square ABCD, we can use the formula:
A = s^2
where s is the side length of the square.
From the previous calculations, we found that the side length of square ABCD is 13 feet.
Substituting s = 13 into the formula, we have:
A = 13^2
A = 169
Therefore, the area of Square ABCD is 169 square feet.