How to Graph Triangles and Quadrilaterals?

Step by Step guide to graphing triangles and quadrilaterals

It is better to get familiar with triangles and quadrilaterals before graphing them:

What is a triangle?

A triangle is a simple polygon with \(3\) sides and \(3\) interior angles. It is one of the basic shapes in geometry in which \(3\) vertices are connected and denoted by a symbol \(△\). Observe the triangle \(PQR\) given below which shows the sides, the vertices, and the interior angles of a triangle.

What is a quadrilateral? 

A quadrilateral is a polygon with four sides, four angles, and four vertices. Whenever we name a quadrilateral, we must consider the order of the vertices. For example, the following quadrilateral should be named \(ABCD\), \(BCDA\), \(ADCB\), or, \(DCBA\). It cannot be named \(ACBD\) or \(DBAC\), since they change the order of the vertices in which a quadrilateral is formed. The following quadrilateral \(ABCD\) has four sides: \(AB, BC, CD, DA\), and two diagonals: \(AC\) and \(BD\).

How to graph triangles and quadrilaterals?

The following steps will be useful to graph triangles and quadrilaterals on the coordinate plane:

1. Mark the given points on the graph sheet one by one.

• \((x, y) \rightarrow\)  Choose the first quadrant
• \((-x, y) \rightarrow\) Choose the second quadrant
• \((-x, -y)\rightarrow\) Choose the third quadrant
• \((x, -y) \rightarrow\) Choose the fourth quadrant

2. Join the marked points.

3. Name the vertices.

Graphing Triangles and Quadrilaterals – Example 1:

Graph the triangle with vertices \((2, -3)\), \((-6, -7)\) and \((-8, -3)\).

Solution:

\((2, -3)\rightarrow (x, -y)\rightarrow\) lies in the fourth quadrant

\((-6, -7)\rightarrow (-x, -y) \rightarrow\) lies in the third quadrant

\((-8, -3) \rightarrow (-x, -y)\rightarrow\) lies in the third quadrant

By plotting the given points, we got above triangle \(ABC\).

Exercises for Graphing Triangles and Quadrilaterals

Graph following shapes.

• \(\color{blue}{(8, 3), (0, -1), (-2, 3), (6, 7)}\)

• \(\color{blue}{(-7, -5), (-4, 3), (5, 6), (2, –2)}\) 

• \(\color{blue}{(8, 3), (0, -1), (-2, 3), (6, 7)}\)

• \(\color{blue}{(-7, -5), (-4, 3), (5, 6), (2, –2)}\)