A square garden has the end points listed below. Plot and label these points on the grid:
(-7,6)
(-2,-6)
(10,-1)
(5,11)
Connect the points to create Square ABCD.
Use the Pythagorean Theorem to find the side length, s, of Square ABCD in feet.
S = ___feet
Use the formula, A=s^2. To find the area of Square ABCD
A = ___feet^2
To start, let's plot the given points on a Cartesian plane:
Point A: (-7, 6)
Point B: (-2, -6)
Point C: (10, -1)
Point D: (5, 11)
To connect these points to form a square:
Connect A to B
Connect B to C
Connect C to D
Connect D to A
Unfortunately, I cannot draw an actual plot here in the text, but you can draw a grid and plot these points on paper or using a graphic tool, forming a square.
Next, we'll calculate the side length of the square using the Pythagorean theorem. You can choose any two adjacent points to do this. Let's use points A (-7, 6) and B (-2, -6), which are connected to form one side of the square.
Using the distance formula d = √((x2 - x1)² + (y2 - y1)²), which is derived from the Pythagorean theorem, we can calculate the distance between A and B:
d_AB = √((-2 - (-7))² + (-6 - 6)²)
d_AB = √((5)² + (-12)²)
d_AB = √(25 + 144)
d_AB = √169
d_AB = 13 feet
So the side length s of Square ABCD is 13 feet.
Now let's calculate the area of the square using the formula A = s^2:
A = (13 feet)^2
A = 169 feet^2
Thus, the area of Square ABCD is 169 square feet.