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 = ________feet
4. Use the area formula, 𝐴𝐴 = 𝑠𝑠2, to find the area of Square ABCD.
A = ________feet2
To plot the points on the grid, we can use a coordinate plane. The x-axis represents the horizontal direction, and the y-axis represents the vertical direction. The origin (0,0) is at the center of the grid.
a. Point A (-7, 6) can be located by moving 7 units to the left on the x-axis and 6 units up on the y-axis. Plot the point A at (-7, 6).
b. Point B (-2, -6) can be located by moving 2 units to the left on the x-axis and 6 units down on the y-axis. Plot the point B at (-2, -6).
c. Point C (10, -1) can be located by moving 10 units to the right on the x-axis and 1 unit down on the y-axis. Plot the point C at (10, -1).
d. Point D (5, 11) can be located by moving 5 units to the right on the x-axis and 11 units up on the y-axis. Plot the point D at (5, 11).
Now, connect the points A, B, C, and D in the given order to create Square ABCD.
To find the side length, s, of Square ABCD, we can use the Pythagorean Theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we can use the distance between points A and B to find the side length of the square. The distance formula between two points (x1, y1) and (x2, y2) is given by:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the distance formula, the distance between A(-7, 6) and B(-2, -6) is:
distance = √((-2 - (-7))^2 + (-6 - 6)^2)
= √(5^2 + (-12)^2)
= √(25 + 144)
= √169
= 13
Therefore, the side length of Square ABCD is 13 feet (s = 13 feet).
To find the area of Square ABCD, we use the formula A = s^2, where s is the side length.
Area = (13 feet)^2
= 13^2
= 169
Therefore, the area of Square ABCD is 169 square feet (A = 169 feet^2).