# Chapter 3 – Coordinate Geometry

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

One of the most enjoyable mathematical principles is known to be Coordinate Geometry. The relation between geometry and algebra is defined by graphs involving curves and lines in Coordinate Geometry (or analytical geometry). It offers geometrical dimensions and helps them to address geometric issues. It is a part of geometry where, using an ordered pair of numbers, the location of points on the plane is defined.

Here, along with the formulas and their derivations, the principles of coordinate geometry (also known as Cartesian geometry) are clarified.

#### History of Coordinate Geometry

The French mathematician René Descartes proposed the method of describing the location of points in this way (1596 – 1650). The coordinates of a point are often referred to as its cartesian system in honor of his work, and the coordination plane is referred to as the Cartesian Coordinate Plane.

#### Overview of Coordinate Geometry

Coordinate geometry (or analytical geometry) is characterized by the use of coordinate system points to analyze geometry. The distance between two points can be found using coordinate geometry, separating lines in the m:n ratio, finding the midpoint of a line, measuring the area of a triangle in the Cartesian plane, etc. In Cartesian geometry, there are some concepts that should be understood properly.

 Coordinate Geometry Terms Description of Coordinate Geometry It is one of the branches of geometry where, using coordinates, the location of a point is defined. Coordinates Coordinates are a series of values that help to illustrate the precise location of a point in the plane of the coordinates. Coordinate Plane A coordination plane is a 2D plane created by the intersection of two x-axis and y-axis perpendicular lines. Formula for Distance The distance between two points found in A(x1,y1) and B is used to find the distance between (x2,y2) Formula for Section It is used in the m:n ratio to segment any line into two segments. The Theorem of Midpoint To find the coordinates in which a line is split into two separate parts, this formula is used.

#### What is a plane of coordinate and coordinate axes?

For both linear and nonlinear equations, you must know how to plot graphs on a plane, from the tables of numbers. Number line, also known as a Cartesian plane, is separated by 2 axes perpendicular to each other into four quadrants, called thel x-axis (horizontal line) and the y-axis (vertical line).

The four quadrants are depicted in the graph below along with their respective values,

(+x, +y): Quadrant 1

(-x, +y): Quadrant 2

(-x, -y): Quadrant3

(+x, -y): Quadrant 4

The point of convergence of the axes is known as the root. A pair of values (x, y) communicates the direction of some point on a plane, and these pairs are known as the coordinates.

#### Cartesian Plane Equation of a Line

A line equation can be interpreted in many ways, of which few are given below,

General Form

Ax + By + C = 0, the general form of a line is given as

• Intercept Form of Slope

Let x, y be the coordinate of a line moving through a point, m be the slope of a line, and c be the y-intercept, then the line equation is given by:

y = mx + c

• Intercept form of a line

Consider a and b, respectively, the x-intercept and y-intercept of a line, so the line equation is represented as,

x + y = 1

Abscissa & Ordinate Signs Of Quadrant

To represent the position of a point on a graph, the abscissa and the ordinate are used. The horizontal value or value of the X-axis is the abscissa, while the ordinate is the vertical value, i.e. the value of the Y-axis. In an ordered pair, for instance (2, 3), 2 is abscissa and 3 is ordinate.

#### Conclusion

In this chapter, we learned about the basics of coordinate geometry. We learned about the quadrants and ways to plot a point in cartesian system. We learned these concepts would be used in mathematical questions.

#### FAQs

• What are coordinates in coordinate geometry?

The point of convergence of the axes is known as the root. A pair of values (x, y) communicates the direction of some point on a plane, and these pairs are known as the coordinates.

• What is the formula of coordinate geometry?

A line equation can be interpreted in many ways, of which few are given below,

General Form

Ax + By + C = 0, the general form of a line is given as

• Intercept Form of Slope

Let x, y be the coordinate of a line moving through a point, m be the slope of a line, and c be the y-intercept, then the line equation is given by:

y = mx + c

• Intercept form of a line

Consider a and b, respectively, the x-intercept and y-intercept of a line, so the line equation is represented as,

x + y = 1

• Where we use coordinate geometry?

To give a link between algebra and geometry with the use of graphs of lines and curves, coordinate geometry is required. It is a valuable branch of mathematics that typically allows one to find points on a plane. In addition, in the areas of trigonometry, calculus, dimensional geometry, and more, it still has numerous applications.

• How do you read coordinates?

Coordinates are pairs of numbers ordered; the first number represents the point on the x-axis and the second the point on the y-axis. You usually go over first and then up when reading or plotting coordinates,

• Why is coordinate geometry important?

One of the most important and thrilling principles of mathematics is coordination geometry. It offers, by graphs of lines and curves, a relation between algebra and geometry. This allows the algebraic solving of geometric issues and offers geometric insights into algebra.

To learn more about coordinate geometry through simple, interactive, and explanatory visualizations, try the MSVgo app.

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• Algebra – Arithmatic Progressions
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### Middle School Math

• Addition
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