Question

Rectangle has the points A:(-6,-2) B:(-2,-2)C:(-2,-5)D:(-6,-5)

Answer 1

To analyze the rectangle defined by the points \( A(-6,-2) \), \( B(-2,-2) \), \( C(-2,-5) \), and \( D(-6,-5) \), we can verify the properties of the rectangle and calculate its dimensions.

1. **Vertices**:
- A: \((-6, -2)\)
- B: \((-2, -2)\)
- C: \((-2, -5)\)
- D: \((-6, -5)\)

2. **side lengths**:
- The length of side \( AB \) (horizontal length) can be calculated as:
\[
AB = |-2 - (-6)| = |-2 + 6| = |4| = 4
\]
- The length of side \( AD \) (vertical length) can be calculated as:
\[
AD = |-5 - (-2)| = |-5 + 2| = |-3| = 3
\]

3. **Area**:
The area \( A \) of the rectangle is given by the product of its lengths:
\[
A = AB \times AD = 4 \times 3 = 12
\]

4. **Perimeter**:
The perimeter \( P \) of the rectangle is given by the formula:
\[
P = 2(AB + AD) = 2(4 + 3) = 2 \times 7 = 14
\]

5. **Coordinates and characteristics**:
- The rectangle has vertical sides (AD and BC) and horizontal sides (AB and CD).
- The opposite sides are equal, confirming it is indeed a rectangle.

So, the dimensions of the rectangle are:
- Length: 4
- Width: 3
- Area: 12
- Perimeter: 14

The rectangle is positioned in the coordinate plane with \( A \) and \( B \) on the same horizontal line at \( y = -2 \), and \( C \) and \( D \) on the same horizontal line at \( y = -5 \).