Question

In rectangle ABCD, point A is at (-1,-1) and point B is at (1,2). A diagonal is drawn from point B to point D and it measures 6 units long. Using this information determine the perimeter of the rectangle. Round your answer to the nearest tenth. (1 point)
perimeter =

Answer 1

To find the perimeter of rectangle ABCD where point A is at (-1, -1) and point B is at (1, 2), and the length of diagonal BD is 6 units, we can follow these steps:

1. **Identify Points and Diagonal:**
Let’s assign points based on the rectangle:

- A = (-1, -1)
- B = (1, 2)

We need to find points C and D such that B and D form one diagonal of the rectangle, and A and C form the other.

2. **Calculate the Length of the Diagonal:**
The formula for the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Since we have point B and we are assuming point D as \((x, y)\), we know:
\[
\sqrt{(x - 1)^2 + (y - 2)^2} = 6
\]

Squaring both sides gives us:
\[
(x - 1)^2 + (y - 2)^2 = 36
\]

3. **Finding Point D:**
Also, note that since A and B are opposite corners of the rectangle, we can use the coordinates of A to help find D. If C is directly across from A, it can be determined that C = (x_c, y_c) must also satisfy the rectangle configuration, assuming proper alignment.

Knowing the coordinates:
\(y_B - y_A = 2 - (-1) = 3\) (the length in the y-axis)
\(x_B - x_A = 1 - (-1) = 2\) (the length in the x-axis)

This means length AB = 3 and length AD = 2.

4. **Calculating Rectangle Perimeter:**
The perimeter \(P\) of a rectangle can be calculated as:
\[
P = 2 \times (length + width)
\]
where \(length = 3\) (vertical distance) and \(width = 2\) (horizontal distance).

Therefore, the perimeter is:
\[
P = 2 \times (3 + 2) = 2 \times 5 = 10
\]

Hence, the perimeter of rectangle ABCD is:

\[
\text{Perimeter} = 10.0
\]

Rounding to the nearest tenth, the final answer is \(10.0\).