You can use the Pythagorean Theorem to find the area of a square when you know its end points.
A square garden has the end points listed below. Plot and label these points on the grid:
A (−7, 6)B (−2, −6)C (10, −1)D (5, 11)
Connect the points to create Square ABCD
.
Use the Pythagorean Theorem to find the side length, s
, of Square ABCD
.
Use the area formula, A = s2
, to find the area of Square ABCD
.
To plot and label the points on the grid, you can do the following:
1. Create a coordinate grid on a piece of paper or a graphing program.
2. Mark the x-axis and y-axis.
3. Plot point A at (-7, 6).
4. Plot point B at (-2, -6).
5. Plot point C at (10, -1).
6. Plot point D at (5, 11).
7. Draw lines to connect the points A, B, C, and D, forming a square ABCD.
To find the side length (s) of Square ABCD using the Pythagorean Theorem, you can use the following formula:
s^2 = (x2 - x1)^2 + (y2 - y1)^2
where (x1, y1) and (x2, y2) are the coordinates of two points on the same side of the square.
Let's find the side length using the coordinates of points A and B:
s^2 = (-2 - (-7))^2 + (-6 - 6)^2
= (5)^2 + (-12)^2
= 25 + 144
= 169
Taking the square root of both sides, we get:
s = √169
= 13
Therefore, the side length of Square ABCD is 13 units.
To find the area of Square ABCD, you can use the formula A = s^2, where s is the side length:
A = (13)^2
= 169
Therefore, the area of Square ABCD is 169 square units.
To plot the points on the grid, follow these steps:
1. Draw a grid with x and y axes.
2. Locate point A at (-7, 6) on the grid. Label it as point A.
3. Locate point B at (-2, -6) on the grid. Label it as point B.
4. Locate point C at (10, -1) on the grid. Label it as point C.
5. Locate point D at (5, 11) on the grid. Label it as point D.
Now, connect the points to create Square ABCD.
To find the side length, s, of Square ABCD using the Pythagorean theorem, follow these steps:
1. Find the length of AB using the formula: AB = sqrt((x2 - x1)^2 + (y2 - y1)^2), where A is (-7, 6) and B is (-2, -6).
- AB = sqrt((-2 - (-7))^2 + (-6 - 6)^2)
- AB = sqrt(5^2 + (-12)^2)
- AB = sqrt(25 + 144)
- AB = sqrt(169)
- AB = 13
2. Since Square ABCD is a square, all sides are of equal length. Therefore, the side length, s, of Square ABCD is 13 units.
To find the area of Square ABCD using the area formula, A = s^2, follow these steps:
1. Substitute the value of the side length, s, into the formula: A = 13^2.
- A = 169
Therefore, the area of Square ABCD is 169 square units.
To plot and label the end points on the grid, you can use a coordinate plane. The x-axis represents the horizontal axis, and the y-axis represents the vertical axis.
Let's plot the points on the grid:
Point A: (-7, 6)
Point B: (-2, -6)
Point C: (10, -1)
Point D: (5, 11)
Now, connect the points in order to form Square ABCD on the grid.
To find the side length of Square ABCD using the Pythagorean Theorem, we need to calculate the distance between two of its vertices. Let's find the distance between points A and B.
Using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
Substituting the coordinates of points A and B into the formula:
d = √[(-2 - (-7))² + (-6 - 6)²]
= √[5² + (-12)²]
= √[25 + 144]
= √169
= 13
Therefore, the distance between points A and B, which is also the side length of Square ABCD, is 13 units.
Now, to find the area of Square ABCD, we use the formula A = s², where s is the side length.
Since we found earlier that the side length is 13, we can calculate the area:
A = 13²
= 169 square units
Thus, the area of Square ABCD is 169 square units.