Rectangle $$ A B C D $$ has an area of 18 square units with $$ A(-5,5) $$ and $$ B(1,5) $$ 1. What are the dimensions of the rectangle? 2. What are the remaining two points that form the rectangle? For full credit, you must: - Answer all parts of the question. - Show your work - Show any formulas that you used.

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**Given:**
- Rectangle $$ ABCD $$ has an area of 18 square units.
- Points $$ A(-5, 5) $$ and $$ B(1, 5) $$.

### 1. **Finding the Dimensions of the Rectangle**

**Step 1: Calculate the Length of Side $$ AB $$**

Since points $$ A $$ and $$ B $$ have the same $$ y $$-coordinate, $$ AB $$ is a horizontal side.

- **Coordinates:**
  - $$ A(-5, 5) $$
  - $$ B(1, 5) $$

- **Length Formula (Distance between two points on a horizontal line):**
  $$
  \text{Length} = |x_2 - x_1|
  $$

- **Calculation:**
  $$
  \text{Length } AB = |1 - (-5)| = |1 + 5| = 6 \text{ units}
  $$

**Step 2: Determine the Width Using the Area**

- **Area Formula for Rectangle:**
  $$
  \text{Area} = \text{Length} \times \text{Width}
  $$

- **Given Area:**
  $$
  18 = 6 \times \text{Width}
  $$

- **Solve for Width:**
  $$
  \text{Width} = \frac{18}{6} = 3 \text{ units}
  $$

**Answer to Part 1:**
- **Dimensions of the Rectangle:** Length = 6 units, Width = 3 units.

### 2. **Finding the Remaining Two Points $$ C $$ and $$ D $$**

**Understanding the Rectangle's Orientation:**

- Points $$ A $$ and $$ B $$ are horizontally aligned.
- The rectangle can extend either **upwards** or **downwards** from side $$ AB $$.

We'll consider both possibilities.

**Case 1: Rectangle Extends Upwards (Positive $$ y $$-direction)**

- **Point $$ D $$:** Located directly above $$ A $$.
  $$
  D = (-5, 5 + 3) = (-5, 8)
  $$
  
- **Point $$ C $$:** Located directly above $$ B $$.
  $$
  C = (1, 5 + 3) = (1, 8)
  $$

**Case 2: Rectangle Extends Downwards (Negative $$ y $$-direction)**

- **Point $$ D $$:** Located directly below $$ A $$.
  $$
  D = (-5, 5 - 3) = (-5, 2)
  $$
  
- **Point $$ C $$:** Located directly below $$ B $$.
  $$
  C = (1, 5 - 3) = (1, 2)
  $$

**Conclusion:**

Without additional information on the rectangle's orientation, both cases are valid. However, typically, we assume the rectangle extends upwards unless specified otherwise.

**Answer to Part 2:**
- **Remaining Points:**
  - $$ C(1, 8) $$
  - $$ D(-5, 8) $$

**Summary:**
1. **Dimensions:** Length = 6 units, Width = 3 units.
2. **Remaining Points:** $$ C(1, 8) $$ and $$ D(-5, 8) $$.
The rectangle has a length of 6 units and a width of 3 units. The remaining two points are $$ C(1, 8) $$ and $$ D(-5, 8) $$.

Rectangle has an area of 18 square units with and

What are the dimensions of the rectangle?

What are the remaining two points that form the rectangle?
For full credit, you must:

Answer all parts of the question.

Show your work

Show any formulas that you used.

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Solución

1. Finding the Dimensions of the Rectangle

2. Finding the Remaining Two Points and

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Rectangle has an area of 18 square units with and What are the dimensions of the rectangle? What are the remaining two points that form the rectangle? For full credit, you must: Answer all parts of the question. Show your work Show any formulas that you used.