Question

Given the rectangle ABCD on the coordinate plane. (3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. The length of side AB in simplest radical form is Response area. The length of side BC in simplest radical form is Response area. The area of rectangle ABCD in simplest radical form is

Answer 1

To determine the lengths of the sides of rectangle ABCD and its area, we need the coordinates of the points A, B, C, and D. Let's assume the coordinates of the vertices are as follows:

- A(x1, y1)
- B(x2, y1)
- C(x2, y2)
- D(x1, y2)

### Length of Side AB
The length of side AB can be calculated as the distance between points A and B. Given both points share the same y-coordinate (y1):

\[
\text{Length of AB} = |x2 - x1|
\]

### Length of Side BC
The length of side BC can be calculated as the distance between points B and C. Given both points share the same x-coordinate (x2):

\[
\text{Length of BC} = |y2 - y1|
\]

### Area of Rectangle ABCD
The area of rectangle ABCD can be determined by multiplying the lengths of sides AB and BC:

\[
\text{Area} = \text{Length of AB} \times \text{Length of BC} = |x2 - x1| \times |y2 - y1|
\]

Since the coordinates were not supplied, you would plug in the specific x1, x2, y1, and y2 values to arrive at your answers.

### Final Responses
1. The length of side AB in simplest radical form is **|x2 - x1|**.
2. The length of side BC in simplest radical form is **|y2 - y1|**.
3. The area of rectangle ABCD in simplest radical form is **|x2 - x1| × |y2 - y1|**.

If you have specific coordinates, please provide them, and I can give you numeric values.