Y. 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12

Question

X. 1 2 3 4 5 6 7 8 9 10 11 12 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12
1. A square garden has the ends 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)

Answer 1

To plot the points of the square garden on the grid, we can take the given coordinates and mark them accordingly.

Here's how the points are:

• A(-7, 6)
• B(-2, -6)
• C(10, -1)
• D(5, 11)

Steps to plot the points:

1. Point A (-7, 6):

   • Move 7 units to the left on the X-axis and 6 units up on the Y-axis. Mark this point as A.

2. Point B (-2, -6):

   • Move 2 units to the left on the X-axis and 6 units down on the Y-axis. Mark this point as B.

3. Point C (10, -1):

   • Move 10 units to the right on the X-axis and 1 unit down on the Y-axis. Mark this point as C.

4. Point D (5, 11):

   • Move 5 units to the right on the X-axis and 11 units up on the Y-axis. Mark this point as D.

Now let's visually describe the grid:

1. X-Axis:

   • Left of the origin (0,0) represents negative values (from -12 to -1).
   • Right of the origin represents positive values (from 1 to 12).

2. Y-Axis:

   • Below the origin represents negative values (from -12 to -1).
   • Above the origin represents positive values (from 1 to 12).

Labeling on the Grid:

• After plotting those points, label each with their corresponding letter (A, B, C, D).

Sketch of the Grid:

 Y
12 |                       D(5,11)
11 |
10 |
 9 |
 8 |
 7 |
 6 |       A(-7,6)
 5 |
 4 |
 3 |
 2 |
 1 |
 0 |---------|---------|---------|---------|----------> X
-1 |                     C(10,-1)
-2 |
-3 |
-4 |
-5 |
-6 |           B(-2,-6)
-7 |
-8 |
-9 |
-10|
-11|
-12|
     -12    -11    -10    -9     -8     -7    -6    -5    -4    -3    -2    -1     0    1    2    3    4    5     6    7     8    9    10    11    12

In this sketch, you would see each point plotted based on their coordinates with labels A, B, C, and D marking their locations. Feel free to adjust the scale of the axes or the layout to meet your specific requirements!

Answer 2

2. Connect the points to create square ABCD.

Answer 3

To connect the points A, B, C, and D to form square ABCD, we need to establish the order of the points based on their positions. From the coordinates provided, it appears the points do not naturally form a square based on the standard geometric definition. Instead, they can be connected in a way that creates either a non-square quadrilateral or potentially a shape that resembles a square more closely based on the relative positions.

Let’s clarify the points again based on their coordinates:

• A(-7, 6)
• B(-2, -6)
• C(10, -1)
• D(5, 11)

Plotting Steps:

1. Place the points on the grid as described previously:
   • A at (-7, 6)
   • B at (-2, -6)
   • C at (10, -1)
   • D at (5, 11)

Connecting Points:

To visualize the connections:

1. Connect point A to point D.
2. Connect point D to point C.
3. Connect point C to point B.
4. Finally, connect point B to point A.

Resulting Connections:

While the connections may visually appear like a polygon, they will not form a perfect square. They will still form a quadrilateral based on the points you've provided.

Here’s the order you would connect them:

• A → D
• D → C
• C → B
• B → A

Visual Representation of the Connections:

 Y
12 |                       D(5,11)
11 |
10 |
 9 |
 8 |
 7 |       A(-7,6)
 6 |
 5 |
 4 |
 3 |
 2 |
 1 |
 0 |---------|---------|---------|---------|----------> X
-1 |                     C(10,-1)
-2 |
-3 |
-4 |
-5 |
-6 |           B(-2,-6)
-7 |
-8 |
-9 |
-10|
-11|
-12|
     -12    -11    -10    -9     -8     -7    -6    -5    -4    -3    -2    -1     0    1    2    3    4    5     6    7     8    9    10    11    12

Connecting the Points:

• Draw a line segment from A to D.
• Draw a line segment from D to C.
• Draw a line segment from C to B.
• Draw a line segment from B back to A.

Conclusion:

This will create a quadrilateral connecting the points but will not form a perfect square based on the coordinates provided. If these points were intended to form a specific shape, please ensure the points are correct for a square or provide more details for adjustment or clarification!

Answer 4

3. Use the Pythagorean theorem to find the side length, s, of square ABCD in feet.
S=_____feet

Answer 5

To use the Pythagorean theorem to find the side length \( s \) of square ABCD, we first need to determine a pair of adjacent points from the list given and calculate the distance between them.

Given Points:

• A(-7, 6)
• B(-2, -6)
• C(10, -1)
• D(5, 11)

Determine Side Length:

For a square, the sides should be equal. Let's calculate the distance between two adjacent points. We can use Points A and B or any pair you choose.

Distance Formula:

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Calculating Distance (Using Points A and B):

• A(-7, 6) and B(-2, -6)
• \(x_1 = -7, y_1 = 6\)
• \(x_2 = -2, y_2 = -6\)

Plugging the values into the distance formula:

\[ d = \sqrt{((-2) - (-7))^2 + ((-6) - 6)^2} \] \[ = \sqrt{(-2 + 7)^2 + (-6 - 6)^2} \] \[ = \sqrt{(5)^2 + (-12)^2} \] \[ = \sqrt{25 + 144} \] \[ = \sqrt{169} \] \[ = 13 \]

Conclusion:

The side length \( s \) of square ABCD is \( s = 13 \) feet.

So, the answer is: \( S = 13 \) feet.

Answer 6

4. Use the area formula, A=s^2, to find the area of square ABCD.
A=_____feet^2

Answer 7

To find the area \( A \) of square ABCD, we can use the area formula for a square, which is:

\[ A = s^2 \]

Given:

• The side length \( s = 13 \) feet (from our previous calculation).

Calculating the Area:

\[ A = (13)^2 = 169 \]

Conclusion:

The area of square ABCD is:

\[ A = 169 \text{ feet}^2 \]

So, the answer is: \( A = 169 \) feet².