To assess the situation given in your question, we can start with the provided points and follow through the steps logically.
Step 1: Plot and Label the Points
- Point A (-7, 6)
- Point B (-2, -6)
- Point C (10, -1)
- Point D (5, 11)
These points can be plotted on a coordinate grid. Hereβs a brief description of where they are located:
- A is in the second quadrant (left and above the origin).
- B is in the fourth quadrant (right and below the origin).
- C is in the first quadrant (right and above the origin).
- D is in the second quadrant (left and above the origin, slightly to the right of A).
Step 2: Connect the Points
To form a square, we need to check if the distance between the points suggests a square. We can pair the points as follows to visualize potential sides and the diagonal:
- AB
- BC
- CD
- DA
Step 3: Calculate the Side Length Using Pythagorean Theorem
To find the side length, use the distance formula, which is derived from the Pythagorean theorem:
\( s = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
Let's calculate each of the sides:
-
AB \[ s_{AB} = \sqrt{((-2) - (-7))^2 + ((-6) - 6)^2} = \sqrt{(5)^2 + (-12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \text{ feet} \]
-
BC \[ s_{BC} = \sqrt{(10 - (-2))^2 + ((-1) - (-6))^2} = \sqrt{(12)^2 + (5)^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \text{ feet} \]
-
CD \[ s_{CD} = \sqrt{((5) - (10))^2 + ((11) - (-1))^2} = \sqrt{(-5)^2 + (12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \text{ feet} \]
-
DA \[ s_{DA} = \sqrt{((-7) - (5))^2 + ((6) - (11))^2} = \sqrt{(-12)^2 + (-5)^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \text{ feet} \]
Result for Side Length
Since we calculated all sides and they are consistent, the side length \( s \) of Square ABCD is:
\[ s = 13 \text{ feet} \]
Step 4: Area Calculation
To find the area \( A \) of the square, we can use the formula:
\[ A = s^2 = 13^2 = 169 \text{ feet}^2 \]
Final Answers
- \( s = 13 \) feet
- \( A = 169 \) feetΒ²
You can then summarize like this:
- \( s = 13 \) feet
- \( A = 169 \) feetΒ²
1 answer