A square garden has the endpoints 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 = 13 feet
Use the formula, A=s^2. To find the area of Square ABCD
A = 169 feet^2
show work
To plot the points for Square ABCD:
1. Start by drawing a grid that can accommodate the given coordinates.
2. Plot the four endpoints as follows:
A: (-7, 6)
B: (-2, -6)
C: (10, -1)
D: (5, 11)
3. Connect the points in the order given to form a square (ABCD).
Unfortunately, I can't plot the graph for you, but you can do this on a piece of graph paper or using any graphing software.
To find the side length, s, of Square ABCD using the Pythagorean Theorem:
Let's consider two adjacent vertices of the square, A and B. The side length of the square will be the distance between these two points.
The distance between two points (x1, y1) and (x2, y2) in a plane is given by the formula derived from the Pythagorean Theorem:
Distance, d = √[(x2 - x1)² + (y2 - y1)²]
Using the coordinates A (-7, 6) and B (-2, -6), we substitute them into the formula:
s = √[(-2 - (-7))² + (-6 - 6)²]
s = √[(5)² + (-12)²]
s = √[25 + 144]
s = √169
s = 13 feet
So the length of one side of the square is 13 feet.
Now, to find the area, A, of Square ABCD, we use the formula:
A = s^2
Substitute the side length into the formula:
A = (13 feet) ^ 2
A = 169 feet^2
Thus, the area of Square ABCD is 169 square feet.