1. **State the problem:** We are given four vertices of a rectangle on the coordinate plane: $(-2, 1)$, $(2, 1)$, $(-2, -1)$, and $(2, -1)$. We want to understand the properties of this rectangle. 2. **Identify the shape and its properties:** The vertices form a rectangle centered at the origin $(0,0)$, symmetric about both the x-axis and y-axis. 3. **Calculate the length and width:** - Length along the x-axis: distance between $(-2, y)$ and $(2, y)$ is $$2 - (-2) = 4$$. - Width along the y-axis: distance between $(x, 1)$ and $(x, -1)$ is $$1 - (-1) = 2$$. 4. **Confirm the center:** The midpoint of the diagonal from $(-2, 1)$ to $(2, -1)$ is $$\left(\frac{-2 + 2}{2}, \frac{1 + (-1)}{2}\right) = (0, 0)$$, confirming the rectangle is centered at the origin. 5. **Summary:** The rectangle extends from $x = -2$ to $x = 2$ and from $y = -1$ to $y = 1$, with length 4 and width 2, centered at the origin. Final answer: The rectangle has length 4, width 2, and is centered at $(0,0)$ symmetric about both axes.