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.

To solve for the dimensions and the remaining points of rectangle \( ABCD \), we will start by finding the length of sides and then determine the coordinates of the remaining vertices. **1. Finding the dimensions of the rectangle:** The points \( A(-5, 5) \) and \( B(1, 5) \) lie on the same horizontal line because they share a \( y \)-coordinate of \( 5 \). The length of side \( AB \) is calculated using the distance formula for points along the same horizontal line: \[ \text{Length of } AB = |x_B - x_A| = |1 - (-5)| = |1 + 5| = |6| = 6 \text{ units} \] Next, we know the area of rectangle \( ABCD \) is given as \( 18 \) square units. The area of a rectangle is calculated by the formula: \[ \text{Area} = \text{Length} \times \text{Width} \] \[ 18 = 6 \times \text{Width} \] To find the width, we rearrange this equation: \[ \text{Width} = \frac{18}{6} = 3 \text{ units} \] Thus, the dimensions of the rectangle are: - Length = \( 6 \) units - Width = \( 3 \) units **2. Finding the remaining two points \( C \) and \( D \):** Since \( AB \) is a horizontal side, the remaining two points \( C \) and \( D \) will be vertically aligned with \( A \) and \( B \). Since the width is \( 3 \) units, we will add and subtract \( 3 \) from the \( y \)-coordinates of points \( A \) and \( B \). We can calculate the coordinates: - For point \( A(-5, 5) \), the possible coordinates for point \( D \): - \( D(-5, 5 - 3) \) or \( D(-5, 2) \) - For point \( B(1, 5) \), the possible coordinates for point \( C \): - \( C(1, 5 - 3) \) or \( C(1, 2) \) Thus, the remaining two points that form the rectangle are: - \( C(1, 2) \) and \( D(-5, 2) \). In summary, the dimensions of the rectangle are \( 6 \) units length and \( 3 \) units width, and the coordinates of the points are: - \( A(-5, 5) \) - \( B(1, 5) \) - \( C(1, 2) \) - \( D(-5, 2) \).