We have image with numbers
Y 12 to lowest -12
X lowest -12 to 12
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.
s=\ f eet
4. Use the area formula, A = s ^ 2 to find the area of Square ABCD.
A=\ f ec * t ^ 2
To plot and label the points on the grid, follow these steps:
1. Draw a grid with the Y-axis ranging from 12 to -12 and the X-axis ranging from -12 to 12.
2. Label the X-axis with numbers from -12 to 12 and the Y-axis with numbers from 12 to -12.
3. Plot each point by locating the corresponding X and Y values on the grid:
- Point A: (-7, 6) - Locate -7 on the X-axis and 6 on the Y-axis. Mark this point.
- Point B: (-2, -6) - Locate -2 on the X-axis and -6 on the Y-axis. Mark this point.
- Point C: (10, -1) - Locate 10 on the X-axis and -1 on the Y-axis. Mark this point.
- Point D: (5, 11) - Locate 5 on the X-axis and 11 on the Y-axis. Mark this point.
To connect the points and create Square ABCD:
1. Start at point A and draw a line segment connecting it to point B.
2. From point B, connect it to point C using another line segment.
3. From point C, connect it to point D using a third line segment.
4. Finally, connect point D back to point A to complete the square.
To find the side length, s, of Square ABCD using the Pythagorean Theorem:
1. Identify any two adjacent points on the square (e.g., points A and B).
2. Calculate the difference between their X-coordinates: -7 - (-2) = -5.
3. Calculate the difference between their Y-coordinates: 6 - (-6) = 12.
4. Use the Pythagorean Theorem (a^2 + b^2 = c^2) to find the length of the hypotenuse (c), which represents the side length of the square:
c^2 = (-5)^2 + 12^2
c^2 = 25 + 144
c^2 = 169
c = 13 (rounded to the nearest whole number)
So, the side length of square ABCD is 13 feet, meaning s = 13 feet.
To find the area of Square ABCD using the area formula (A = s^2):
1. Substitute the value of the side length (s = 13 feet) into the formula:
A = (13 feet)^2
A = 13^2 = 169 square feet
Therefore, the area of Square ABCD is 169 square feet.