To solve the problem, we need to follow the steps provided.
1. Plot and Label the Points
Let's plot the given points on the grid:
- Point A: (-7, 6)
- Point B: (-2, -6)
- Point C: (10, -1)
- Point D: (5, 11)
2. Connect the Points to Create Square ABCD
Upon plotting these points on the coordinate grid, you will want to connect them in the order A, B, C, D to create the shape of the square. It’s important to note that the points need to correspond to the correct arrangement of a square.
3. Use the Pythagorean Theorem to Find Side Length, s
To find the length of one side of the square, we should calculate the distance between two adjacent points using the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
We'll need to identify two points that would give us the side length of the square. For this case, let's use points A and B:
- A: (-7, 6)
- B: (-2, -6)
Now, substituting into the formula: \[ s = d(A, B) = \sqrt{((-2) - (-7))^2 + ((-6) - 6)^2} \] Calculating: \[ s = \sqrt{(-2 + 7)^2 + (-6 - 6)^2} \] \[ s = \sqrt{(5)^2 + (-12)^2} \] \[ s = \sqrt{25 + 144} \] \[ s = \sqrt{169} \] \[ s = 13 \text{ feet} \]
4. Use the Area Formula, A = s^2
Now, using the area formula for a square: \[ A = s^2 = 13^2 = 169 \text{ feet}^2 \]
Final Results
Now we can summarize our findings:
- s = 13 feet
- A = 169 feet²
So the answers to your questions are:
- s = 13 feet
- A = 169 feet²
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