Polygons on the Coordinate Plane

Polygons are two-dimensional shapes that are defined by straight sides and closed lines. They can have any number of sides greater than or equal to three.The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges. The point where two line segments meet is called vertex or corners, henceforth an angle is formed.

An example of a polygon is a triangle with three sides. A circle is also a plane figure but it is not considered a polygon, because it is a curved shape and does not have sides or angles. Therefore, we can say, all the polygons are 2d shapes but not all the two-dimensional figures are polygons. Some common examples of the polygon include:

• Triangle: Three sides and three angles.
• Square: Four sides of equal length and four right angles.
• Rectangle: Four sides with two pairs of equal-length sides and four right angles.
• Pentagon: Five sides and five angles.
• Hexagon: Six sides and six angles.

Polygons are used in many mathematical and real-world applications, such as computer graphics, architecture, and engineering. In these applications, the measurement and manipulation of polygon shapes are often important. The properties of polygon shapes, such as their perimeter, area, and interior angles, can be calculated and used in various ways.

A coordinate plane is a two-dimensional mathematical system to locate points, plot graphs, and solve equations. It is defined by two perpendicular lines, called the x-axis and y-axis, which intersect at a point called the origin. The x-axis runs horizontally and the y-axis runs vertically. Each point in the coordinate plane can be described by a pair of numbers, called its coordinates, which give its position relative to the origin. The x-coordinate of a point represents its position on the x-axis and the y-coordinate of a point represents its position on the y-axis. Points in the coordinate plane can be represented graphically and used to plot mathematical functions and study geometric shapes.

Plotting a Polygon on the Coordinate Plane

To plot a polygon on the coordinate plane, you need to know the coordinates of its vertices. A polygon with n vertices has n points in the coordinate plane, each with its own x and y coordinates.

To plot a polygon on the coordinate plane, follow these steps:

Identify the vertices of the polygon and write down their coordinates.

Plot each vertex on the coordinate plane by finding its corresponding x and y coordinates.

Connect the vertices in the order in which they are given to form the polygon.

Example 1: Plotting a triangle
Let’s say we have the vertices of a triangle: P(4,5), Q(2,2), and R(5,1). To plot this triangle on the coordinate plane, we first plot each vertex.

P: (4,5)
Q: (2,2)
R: (5,1)

Next, we connect the vertices in the order in which they are given, P to Q to R and R to P, to form the triangle.

Example 2: Plotting a square
Let’s say we have the vertices of a square: A(2,3), B(2,5), C(4,5), and D(4,3). To plot this square on the coordinate plane, we first plot each vertex.

A: (2,3)
B: (2,5)
C: (4,5)
D: (4,3)
Next, we connect the vertices in the order in which they are given, A to B to C to D to A, to form the square.

In this way, you can plot any polygon on the coordinate plane by finding its vertices and connecting them in the order in which they are given.

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