To solve the problem, let's go through each step systematically.
1. Plotting the Points
Let's plot the points A, B, C, and D on the Cartesian grid:
- A (-7, 6)
- B (-2, -6)
- C (10, -1)
- D (5, 11)
Placing these points on a grid:
- Point A is located at (-7, 6).
- Point B is located at (-2, -6).
- Point C is located at (10, -1).
- Point D is located at (5, 11).
2. Connecting the Points
To create Square ABCD, we need to connect the points A, B, C, and D in sequence. However, since it appears these points do not create a square based on their coordinates, let's identify which points should actually form a square.
3. Side Length Calculation
To find the side length \( s \) of the square, we need to identify two adjacent points and use the Pythagorean Theorem, \( s^2 = a^2 + b^2 \).
Let's take two adjacent points, for example:
- A (-7, 6) and D (5, 11).
The distance between points A and D is given by:
\[ s = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Where:
- \( (x_1, y_1) = (-7, 6) \)
- \( (x_2, y_2) = (5, 11) \)
Calculating \( s \):
\[ s = \sqrt{(5 - (-7))^2 + (11 - 6)^2} \] \[ s = \sqrt{(5 + 7)^2 + (5)^2} \] \[ s = \sqrt{12^2 + 5^2} \] \[ s = \sqrt{144 + 25} \] \[ s = \sqrt{169} \] \[ s = 13 \text{ feet} \]
4. Area Calculation
Now, using the area formula for a square \( A = s^2 \):
\[ A = 13^2 = 169 \text{ square feet} \]
Summary of Answers:
- Side length \( s \) of Square ABCD: 13 feet
- Area \( A \) of Square ABCD: 169 square feet
If the points were meant to make a square, it seems either the coordinates were incorrect or the interpretation of the square needs to be recalibrated. The calculated distance of 13 feet for those particular points indicates they do not directly form a square. Please verify the points' arrangements if you want the true square configuration.
2 answers