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.
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 = feet
To visualize the scenario, we can't plot the actual points on a grid here, but I can guide you through the process:
1. Plot the points on a coordinate grid:
a. Plot point A at (-7, 6).
b. Plot point B at (-2, -6).
c. Plot point C at (10, -1).
d. Plot point D at (5, 11).
Note: After plotting these points, you will likely realize that these points do not form a square. However, I will continue the rest of the process assuming they did.
2. Connect the points to create what would be Square ABCD. You would do this by drawing lines between A and D, A and B, B and C, and C and D.
3. Assuming that the points somehow formed a square (which is not the case), you would use the distance formula to find the length of one side of the square. The distance formula in a 2D coordinate plane is:
distance = √((x2 - x1)² + (y2 - y1)²)
If point A and point B formed one side of a square, you would calculate:
distance_AB = √((-2 - (-7))² + (-6 - 6)²)
= √((5)² + (-12)²)
= √(25 + 144)
= √169
= 13
So, if points A and B formed one side of a square, the side length (s) would be 13 feet.
4. Use the area formula for a square, A = s², where s is the side length:
A = s²
A = (13)²
A = 169 square feet
This would be the area of the square with a side length of 13 feet.
However, please note that the given points A, B, C, and D do not actually form a square with equal sides or 90-degree angles at each corner. In reality, you would need to recalculate distances for the given points if you were asked to find the area of a quadrilateral formed by these points.