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). 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 4. Use the area formula, A = s ^ 2 to find the area of Square ABCD. A=\ f eet
Here is the solution:
1. Plotting the points on the grid:
a. Point A (-7, 6)
b. Point B (-2, -6)
c. Point C (10, -1)
d. Point D (5, 11)
Here is the plotted square:
```
| |
----C--|--D-----|
| |
----A--|--------|
| |
B
```
2. Using the Pythagorean Theorem to find the side length, s:
To find the side length, we need to find the distance between two points on a plane, which is given by the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For points A (-7, 6) and B (-2, -6):
d_AB = sqrt((-2 - (-7))^2 + (-6 - 6)^2)
= sqrt(5^2 + (-12)^2)
= sqrt(25 + 144)
= sqrt(169)
= 13
For points B (-2, -6) and C (10, -1):
d_BC = sqrt((10 - (-2))^2 + (-1 - (-6))^2)
= sqrt(12^2 + 5^2)
= sqrt(144 + 25)
= sqrt(169)
= 13
For points C (10, -1) and D (5, 11):
d_CD = sqrt((5 - 10)^2 + (11 - (-1))^2)
= sqrt((-5)^2 + 12^2)
= sqrt(25 + 144)
= sqrt(169)
= 13
For points D (5, 11) and A (-7, 6):
d_DA = sqrt((-7 - 5)^2 + (6 - 11)^2)
= sqrt((-12)^2 + (-5)^2)
= sqrt(144 + 25)
= sqrt(169)
= 13
Since all four sides are equal to 13 feet, the side length of square ABCD is 13 feet.
3. Calculating the area of Square ABCD:
The area of a square is given by the formula:
A = s^2
Substituting the known value of the side length:
A = 13^2
= 169 square feet
Therefore, the area of square ABCD is 169 square feet.