To plot the points on a grid, draw a horizontal x-axis and a vertical y-axis. Then, use the x-coordinate to determine the horizontal position and the y-coordinate to determine the vertical position of each point.
a. Point A is located at (-7, 6).
Plot the point (-7, 6) on the grid.
b. Point B is located at (-2, -6).
Plot the point (-2, -6) on the grid.
c. Point C is located at (10, -1).
Plot the point (10, -1) on the grid.
d. Point D is located at (5, 11).
Plot the point (5, 11) on the grid.
Now that all the points are plotted, draw a line connecting points A, B, C, and D to form a square.
To find the side length of Square ABCD, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In Square ABCD, the diagonal (AC or BD) is the hypotenuse, and the sides of the square (AB, BC, CD, and DA) are the other two sides. Since the side length of the square is the same for all sides, let's denote it as s.
Using the Pythagorean Theorem, we have:
s^2 + s^2 = c^2,
where c is the diagonal length.
Since the diagonal length is the square root of the sum of the squares of the side lengths, we have:
c = √(s^2 + s^2) = √(2s^2) = √2s.
Now, we need to find the value of s by using the given points of the square.
The distance formula can be used to find the distance between two points:
d = √((x2 - x1)^2 + (y2 - y1)^2).
Using the distance formula, we can find the length of the diagonal AC:
AC = √((10 - (-7))^2 + (-1 - 6)^2) = √(17^2 + (-7)^2) = √(289 + 49) = √338.
The length of the diagonal AC is equal to √2s:
√338 = √2s.
Now, we can solve for s:
√2s = √338.
2s = 338.
s = 338/2.
s = 169.
Therefore, the side length of Square ABCD is 169 feet.
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) . Use the Pythagorean Theorem to find the side length, s, of Square ABCD in feet. Area = a2 + b2 = c2 where c is the side length, s.
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