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 = a
2 + b
2 = c
2 where c is the side length, s.
s = feet
I cannot physically draw and display the square on a grid for you here because this is a text-based platform. However, I can guide you through the process so that you can draw it yourself.
1. To plot the points, you'll need a Cartesian coordinate system, which includes both the x-axis (horizontal) and y-axis (vertical). Each point is given as (x, y).
- A is at (-7, 6). You move 7 units to the left (negative x) and 6 units up (positive y) from the origin (0,0) to plot this point.
- B is at (-2, -6). You move 2 units to the left and 6 units down from the origin.
- C is at (10, -1). You move 10 units to the right and 1 unit down from the origin.
- D is at (5, 11). You move 5 units to the right and 11 units up from the origin.
2. To create Square ABCD, you would draw straight lines connecting the points in order A to B, B to C, C to D, and D back to A.
3. To find the side length of the square using the Pythagorean Theorem, you pick two adjacent vertices. The sides have equal lengths in a square, so it doesn't matter which two adjacent vertices you choose. Let's calculate the side length using points A and B. Since points A and B form a vertical edge of the square, we can calculate the side length by finding the difference in the y-coordinates (because the x-coordinates are the same for the entire vertical side).
A is at (-7, 6), and B is at (-2, -6).
The vertical distance (side length) is the difference in the y-coordinates: 6 - (-6) = 6 + 6 = 12 feet.
The side length s of Square ABCD is 12 feet.
As for the equation you provided (Area = a^2 + b^2 = c^2), it looks like a variation of the Pythagorean theorem a^2 + b^2 = c^2, which applies to right triangles, not directly to finding the area of a square. The area of a square is simply the side length squared: Area = s^2. In this case:
Area = s^2 = (12 feet)^2 = 144 square feet.
The area of Square ABCD is 144 square feet.
Use the area formula, 𝐴 = 𝑠
2
, to find the area of Square ABCD.
A = fee
The formula for the area of a square is given by \( A = s^2 \), where \( s \) is the side length of the square.
From the previous explanation, we found that the side length of Square ABCD is \( s = 12 \) feet. Plugging this into the area formula, we get:
\( A = s^2 \)
\( A = (12\ \text{feet})^2 \)
\( A = 144\ \text{square feet} \)
So, the area of Square ABCD is 144 square feet.
To plot the given points on a grid, follow these steps:
1. Draw a grid with x-axis (horizontal) and y-axis (vertical) lines intersecting at the origin (0,0).
2. Locate point A (-7, 6): Move 7 units to the left from the origin on the x-axis and then 6 units upwards on the y-axis. Mark this point as A.
3. Locate point B (-2, -6): Move 2 units to the left from the origin on the x-axis and then 6 units downwards on the y-axis. Mark this point as B.
4. Locate point C (10, -1): Move 10 units to the right from the origin on the x-axis and then 1 unit downwards on the y-axis. Mark this point as C.
5. Locate point D (5, 11): Move 5 units to the right from the origin on the x-axis and then 11 units upwards on the y-axis. Mark this point as D.
Now that we have plotted the points, we can connect them to create Square ABCD by drawing lines between the points in the following order: A -> B -> C -> D -> A.
To calculate the side length of Square ABCD using the Pythagorean Theorem:
1. Identify any two adjacent points, such as A and B.
2. Use the formula a^2 + b^2 = c^2, where a and b are the differences in the x and y coordinates between the two points, and c is the side length. In this case, a = -7 - (-2) = -5 and b = 6 - (-6) = 12.
3. Substitute the values into the formula: (-5)^2 + 12^2 = c^2.
4. Simplify the equation: 25 + 144 = c^2.
5. Add the values: 169 = c^2.
6. Take the square root of both sides to solve for c: √169 = √c^2.
7. Simplify: 13 = c.
Therefore, the side length of Square ABCD is 13 feet.