Two dimensional geometry formulas

Two dimensional geometry formulas  sometimes known as plane geometry formulas , are the branch of geometry concerned with shapes, figures, and their properties in the two-dimensional plane. The plane has two dimensions: length and width, represented by the x-axis (horizontal) and y-axis (vertical) in a Cartesian coordinate system.

The basic ideas of two-dimensional geometry are points, lines, angles, forms (such as triangles, circles, and polygons), and their attributes. Let’s look at some essential aspects:

1. Cartesian Coordinates and Plane

The Cartesian coordinate system is the basis for two-dimensional geometry. The coordinate plane is a flat surface with points specified by a pair of numbers  (x,y).

•  x represents the abscissa (horizontal distance from the origin).
•  y represents the ordinate (vertical distance from the origin).

The origin (0,0) is where the x-axis and y-axis cross.

2. Points and coordinates

• A point is an location in the plane without size or dimension, expressed by coordinates  (x,y).
• The distance between two points (x_1, y_1​) and  (x_2, y_2) is given by the distance formula:

• The midpoint between two points (𝑥_1, 𝑦_ 1)  and (𝑥_ 2, 𝑦_ 2) is the point that divides the segment connecting them into two equal parts.

3. Lines and slopes

A line in the plane can be represented by the following linear equation:

• The slope (𝑚) of a line running through two points (𝑥_1, 𝑦_1)  and (𝑥_2, 𝑦_2)  can be calculated as:

• The equation of a line in slope-intercept form (when the slope $m$ and y-intercept c are known) is:

4. Angles

Angle between two lines: The  angle θ between two lines with slopes of m_1  and 𝑚_2  is as follows:

• The angle between two parallel lines is 0∘, and they both have the same slope.
• The slopes of perpendicular lines are negative reciprocals of one another, meaning that 𝑚_1 𝑚_2 = −1 , and the angle between them is 90∘ .

5. Distance between a point and a line.

The distance between a point P(x_0​,y_0​) and a line Ax+By+C=0 is determined by the formula:

6. Types of 2D Triangle Geometric Figures

A triangle is a three-sided polygon. Triangles can be classified according to angles as follows:

• Acute triangle: All angles less than 90∘
• Right triangle: One angle is 90∘
• Obtuse triangle: One angle is greater than 90∘

A triangle’s area is:

The area of a triangle with vertices A(x_1, y_1), B(x_2, y_2), C(x_3, y_3), and  is as follows:

Quadrilaterals
A four-sided polygon is called a quadrilateral. Among the varieties are:

Square , Rectangular, Parallelogram, trapezium, rhombus
A rectangle’s area is:

Circles
The set of all points in the plane that are equally spaced from a fixed point (the center) is called a circle. The equation for a circle with radius r and center (h,k) is as follows:

The area and circumference of a circle are given by:

Area:

Circumference:

Polygons
A closed figure with straight sides is called a polygon. Among the examples are:

Pentagon (5 sides)
Hexagon (6 sides)
Octagon (8 sides)

The sum of the interior angles of a polygon with $n$ sides is given by:

Sum of interior angles=(n−2)×180∘

7. Conic Sections

Conic sections are curves that can be obtained by intersecting a plane with a cone. Each has a specific general equation.

• Circle:

• Ellipse:

• Parabola:

• Hyperbola:

8. Coordinated Geometry

In Two dimensional geometry formulas , coordinate geometry (also known as analytic geometry) employs the Cartesian coordinate system to algebraically represent and investigate geometric shapes.

For example:

• The distance formula finds the distance between two places.
• The slope of a line indicates its steepness and direction.
• A circle’s equation can be calculated using the distance between the center and a point on the circle.