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: a2 + b2 = c? where c is the side length, s.
1231567811112
Hint: Can you create a right triangle off the left side of square ABCD?
§ =
feet (worth 3 points)
Use the area formula, A = s?, to find the area of
Square ABCD.
A =
feet (worth 3 points)
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: a2 + b2 = c? where c is the side length, s.
1231567811112
Hint: Can you create a right triangle off the left side of square ABCD?
§ =
feet (worth 3 points)
Use the area formula, A = s?, to find the area of
Square ABCD.
A =
feet (worth 3 points)
Answers
GPT-4o mini
Let's go through each part of the question step by step.
### 1. Plot and Label Points A, B, C, and D
The given points are:
- A (-7, 6)
- B (-2, -6)
- C (10, -1)
- D (5, 11)
To plot these points on a grid:
- Point A is located at (-7, 6), which is 7 units left and 6 units up from the origin.
- Point B is located at (-2, -6), which is 2 units left and 6 units down from the origin.
- Point C is located at (10, -1), which is 10 units right and 1 unit down from the origin.
- Point D is located at (5, 11), which is 5 units right and 11 units up from the origin.
You would mark these points on a graph and label them accordingly.
### 2. Connect the Points to Create Square ABCD
To form square ABCD, you would connect the points in order, creating a closed shape:
- Connect A to B,
- Connect B to C,
- Connect C to D,
- Connect D back to A.
### 3. Use the Pythagorean theorem to find the side length
The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (a and b) equals the square of the hypotenuse (c):
\[
a^2 + b^2 = c^2
\]
To find the side length of the square, we need to pick two points that will form a right triangle.
Let’s calculate the lengths of the sides between a couple of the points:
- The distance between points A (-7, 6) and D (5, 11) can be calculated as follows:
Using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
For points A and D:
- \(x_1 = -7\), \(y_1 = 6\)
- \(x_2 = 5\), \(y_2 = 11\)
Calculating the distance:
\[
d = \sqrt{(5 - (-7))^2 + (11 - 6)^2} = \sqrt{(5 + 7)^2 + (11 - 6)^2} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13
\]
Thus, the length of side s is 13 feet.
### Area of Square ABCD
Now to find the area A of square ABCD:
\[
A = s^2 = 13^2 = 169 \text{ square feet}
\]
### Summary of Answers:
- Side length \(s = 13\) feet (worth 3 points)
- Area \(A = 169\) square feet (worth 3 points)
### 1. Plot and Label Points A, B, C, and D
The given points are:
- A (-7, 6)
- B (-2, -6)
- C (10, -1)
- D (5, 11)
To plot these points on a grid:
- Point A is located at (-7, 6), which is 7 units left and 6 units up from the origin.
- Point B is located at (-2, -6), which is 2 units left and 6 units down from the origin.
- Point C is located at (10, -1), which is 10 units right and 1 unit down from the origin.
- Point D is located at (5, 11), which is 5 units right and 11 units up from the origin.
You would mark these points on a graph and label them accordingly.
### 2. Connect the Points to Create Square ABCD
To form square ABCD, you would connect the points in order, creating a closed shape:
- Connect A to B,
- Connect B to C,
- Connect C to D,
- Connect D back to A.
### 3. Use the Pythagorean theorem to find the side length
The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (a and b) equals the square of the hypotenuse (c):
\[
a^2 + b^2 = c^2
\]
To find the side length of the square, we need to pick two points that will form a right triangle.
Let’s calculate the lengths of the sides between a couple of the points:
- The distance between points A (-7, 6) and D (5, 11) can be calculated as follows:
Using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
For points A and D:
- \(x_1 = -7\), \(y_1 = 6\)
- \(x_2 = 5\), \(y_2 = 11\)
Calculating the distance:
\[
d = \sqrt{(5 - (-7))^2 + (11 - 6)^2} = \sqrt{(5 + 7)^2 + (11 - 6)^2} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13
\]
Thus, the length of side s is 13 feet.
### Area of Square ABCD
Now to find the area A of square ABCD:
\[
A = s^2 = 13^2 = 169 \text{ square feet}
\]
### Summary of Answers:
- Side length \(s = 13\) feet (worth 3 points)
- Area \(A = 169\) square feet (worth 3 points)