Basics of 2D geometry

Regular and Irregular 2D Shapes

Two dimensional (2D) can be divided into two parts, regular and irregular, depending on the length and interior angle.The standard 2D shape is when its size and internal angle are the same.The irregular 2D geometry is when its length and interior angle are not equal.

Difference Between 2D Shapes and 3D Shapes

Properties and Basics of 2D Geometry

Two-dimensional (2D) shapes can be quickly drawn on paper. We have many types of irregular and regular 2D geometry. These shapes include rectangle, square, triangle, hexagon, quadrilateral, and pentagon.

Properties of these 2D geometry shapes are: –

Circle

The circle is referred to as a closed figure shape with no edges. Some of the examples are coins, ball wheels, etc. It includes circumference, radius, diameter, etc.

Properties

1. The circle is a full circle with one curved line.
2. Radius is the center of the process to boundaries of the circle
3. Diameter is the longest line in the circle meeting end to end of the circle
4. The circumference is the length of the edge of the circle

Triangle

Triangle is also a 2 D shape. It has a total of three sides and three vertices.

Properties

1.A triangle is defined as a closed figure. It has three sides, three vertices, and three angles.

For example – Traffic signals, nachos, and pyramids.

Square

A square is a four similarly shaped side with an angle equal to 90 degrees. Some real-life things we see in day-to-day life are a chessboard, etc.

Properties

1. All sides are equal in a square.
2. All measure up to 90 degrees on each side
3. For example, all four sides can be summed up as AB=BC=BC=CD

Rectangle

A rectangle is defined as a 2D shape that has four sides. The opposite sides of a rectangle are the same in length and parallel. All four sides are at an angle of 90 degrees. Real-life examples are – Cardboard, duster, etc.

Properties

1. Side – AB = CD
2. Side – AD= BC
3. AB || CD
4. AC || BD

Pentagon

Pentagon is a 2D shape with properties of –

1. All five sides are equal
2. Every interior angle is 108 degree
3. Every exterior grade is 72 degree

Hexagon

A hexagon is a  2D geometry shape with six vertices and angles.

Properties

1. All six sides are equal
2. Every interior angle is 120 degrees
3. Every exterior grade is 60 degrees

Coordinate Geometry in Two-Dimensional Plane

A two-dimensional geometry plane deals with the x and y coordinate plane or Cartesian plane. A coordinate geometry plane has two axes one is horizontal, known as the x-axis, and one is vertical, known as the y axis. A point (x,y), representing the x and y plane where x and y are the coordinates of the point.0 is the origin of the coordinate (0,0).

Distance between two points in 2D geometry.

If we take two points as A(x1,y1) A(x1,y1) and B(x2,y2) B(x2,y2) in an XY plane.

Then the distance between A and B is,

AB=√((x2−x1)2+(y2−y1)2)

For example, we take points A(2,-3) and B(5,1) is,

AB=√(5−2)2+(1−(−3))2=√3 2 +4 2=√25=5 units

 Important Two-Dimensional Coordinate Geometry Terms

• Coordinate axes

The coordinates OX and OY are known as X-axis and Y-axis. These both are also called the axes of coordinates

• Origin

It is a point where two lines( x-axis and y-axis) intersect.

• Abscissa

Any point that is present on the plane, it’s X-coordinate is known as Abscissa.

• Ordinate

Any point on the plane, it’s Y-coordinate is called as Ordinate.

• Coordinate of the Origin

The origin of the coordinates are (0,0) as the distance is zero from both the axes.

• Quadrant

The quadrants are divided into four parts. Each part is divided into 1/4th area.

Examples

Example 1: P (4, 5) and Q(7, – 1) are two points granted to you. Externally, a point R splits the line-segment PQ in the ratio 4:3. Determine its Y-coordinate.

Solution :

P(4,5)=(x1,y1),

Q(7,-1)=(x2,y2)

We know that the segment PQ is divided in the ratio 4:3 by the provided Point R.

m=4, n=3

Using the formula for sections:

R = {[(mx2−nx1)/(m−n)],[(my2−ny1)/(m−n)]}

={((4×7)−(3×4))/(4−3)

((4×7)−(3×4))/(4−3),

(4x−1)−(3×5)/(4−3)

(4x−1)−(3×5)/(4−3)}

={(28 – 12)/1,(-4 – 15)/1}

={16,-19}

The coordinates are (16,-19)

Example 2: Calculate the area of the triangle LMN, which has the vertices L(3, 2), M(4, 2), and N as its vertices (3, 5). 

It is given that L( 3, 2) = ( x1, y1)

             M( 4, 2) = ( x2, y2)

             N( 3, 5) = ( x3, y3)

The covered area of ΔLMN must now be calculated. We have a formula for this.

A = ½ [x1 (y2– y3 )+x2 (y3 – y1)+x3(y1– y2)]

A = ½

3(2–5)+4(5–2)+3(2–2)

3(2–5)+4(5–2)+3(2–2)

A = ½

3x(−3)+4×3

3x(−3)+4×3

A = ½

−9+12

−9+12

A = ½ (3)

         = 3/2 square units.

As a result, the area of  ΔLMN equals 3/2 square units. .

Conclusion

Coordinate geometry is a field of mathematics that uses an ordered pair of integers to assist us precisely find a given position. To answer issues, 2 dimensional geometry uses a combination of geometry and algebra. A 2D shape is considered a standard 2D shape when its size and internal angle are the same. It’s termed irregular 2D geometry when a 2D geometry’s length and interior angle aren’t the same.