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 Response area.

Answer 1

To answer the question, we first need to define the coordinates of points A, B, C, and D for rectangle ABCD. I'll use the general case, where:

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

### Step 1: Finding the Length of Side AB
The length of side AB can be determined using the distance formula \( AB = |x2 - x1| \).
Assuming you know the coordinates of A and B, you can substitute the values.

### Step 2: Finding the Length of Side BC
The length of side BC can be determined using the distance formula \( BC = |y2 - y1| \).
Similarly, substitute the known coordinates to find this length.

### Step 3: Finding the Area of Rectangle ABCD
The area of rectangle ABCD is given by:
\[ \text{Area} = \text{length of } AB \times \text{length of } BC \]

### Example with Coordinates
Assuming:
- A is at (1, 1)
- B is at (5, 1)
- C is at (5, 4)
- D is at (1, 4)

Calculations:
1. **Length of side AB**:
- \( AB = |5 - 1| = 4 \)

2. **Length of side BC**:
- \( BC = |4 - 1| = 3 \)

3. **Area of rectangle ABCD**:
- \( \text{Area} = AB \times BC = 4 \times 3 = 12 \)

### Final Responses
So based on the example coordinates:
- The length of side AB in simplest radical form is: **4**
- The length of side BC in simplest radical form is: **3**
- The area of rectangle ABCD in simplest radical form is: **12**

Make sure to replace these lengths and area with the correct values obtained from the specific coordinates you have for rectangle ABCD.