A. Here are the vertices of rectangle F R O...

a. Here are the vertices of rectangle $F R O G:(-2,5),(-2,1),(6,5),(6,1)$. Find the perimeter of this rectangle. If you get stuck, try plotting the points on a coordinate plane. b. Find the area of the rectangle $F R O G$. c. Here are the coordinates of rectangle $P L A Y:(-11,20),(-11,-3),(-1,20),(-1,-3)$. Find the perimeter and area of this rectangle. See if you can figure out its side lengths without plotting the points.

a. Here are the vertices of rectangle $F R O G:(-2,5),(-2,1),(6,5),(6,1)$. Find the perimeter of this rectangle. If you get stuck, try plotting the points on a coordinate plane.
b. Find the area of the rectangle $F R O G$.
c. Here are the coordinates of rectangle $P L A Y:(-11,20),(-11,-3),(-1,20),(-1,-3)$. Find the perimeter and area of this rectangle. See if you can figure out its side lengths without plotting the points.

Key Concepts

Distance Calculation in the Coordinate Plane

Determining distances between points on a coordinate plane typically involves calculating the difference between corresponding coordinates. For horizontal or vertical distances, the magnitude of the difference is used directly, which simplifies the process of finding side lengths when the movements are parallel to the axes.

Properties of Rectangles

Rectangles are quadrilaterals characterized by having opposite sides that are equal in length and every interior angle measuring 90 degrees. This fundamental property ensures that one can deduce side lengths from coordinates and use this consistent structure to apply geometric formulas uniformly across problems involving rectangles.

Perimeter of a Rectangle

The perimeter of a rectangle is the total distance around its boundary. It is calculated by adding the lengths of all four sides, which can be simplified using the formula 2 × (length + width). This calculation is foundational in geometry for determining the distance around a two?dimensional shape.

Area of a Rectangle

Calculating the area of a rectangle involves multiplying the length by the width, yielding the space contained within the rectangle measured in square units. Understanding area is critical in various applications, such as determining surface extents and solving diverse geometric problems.

Coordinate Geometry

Coordinate geometry, or analytic geometry, involves representing geometric figures using coordinates on a plane. This approach allows one to combine algebra and geometry to compute distances, slopes, and other properties by applying algebraic methods to geometric problems.

Plotting Points

Plotting points on a coordinate plane provides a visual framework for understanding the positions and relationships of geometric figures. This method often serves as a helpful tool for verifying properties and extracting information such as side lengths, orientations, and overall shape structure.

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