Question

1. A square garden has the end points listed below.
Plot and label these points on the grid (worth 4 points) :
1. A (-7, 6)
2. B (-2, -6)
3. C (10, -1)
4. D (5, 11)
2. Connect the points to create Square ABCD. (worth 2 points)
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.
Hint: Can you create a right triangle off the left side of square ABCD?
feet (worth 3 points)
Use the area formula, A = s^2, to find the area of Square ABCD.
A =___feet (worth 3 points)

Answer 1

To solve your problem step by step:

### Step 1: Plot the Points
First, we need to mark the given points on a coordinate grid.

1. Point A: (-7, 6)
2. Point B: (-2, -6)
3. Point C: (10, -1)
4. Point D: (5, 11)

### Step 2: Connect the Points
To connect the points and form a square ABCD, we should draw lines between each consecutive point: A to B, B to C, C to D, and D back to A.

### Step 3: Find the Side Length using the Pythagorean Theorem
Now, let's find the side length of the square. We can use the distance formula which is derived from the Pythagorean theorem:

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Let's find the distance between points A and B:
- A = (-7, 6) and B = (-2, -6)

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

So, the side length \( s \) of Square ABCD is 13 feet.

### Step 4: Calculate the Area
Now, we use the area formula for a square:
\[
A = s^2
\]
Substituting our side length:
\[
A = 13^2 = 169
\]

### Final Answers
- Side Length \( s = 13 \) feet
- Area \( A = 169 \) square feet

Please ensure to plot the points and connect them based on the steps outlined above to visualize Square ABCD accurately.