# Chapter 3 – Coordinate Geometry

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

Introduction

Coordinate geometry is one of the riveting concepts of mathematics. It delineates the link between geometry and Algebra with the help of graphs including, curves and lines. Coordinate Geometry is used by the aviation sector to determine the position of the airplanes. The topics are easier once you understand them. We hope this article helps you understand the concepts. In this article, we discuss coordinate geometry in detail form to help you understand the basics effortlessly.

#### Cartesian System

It is a system through which two or more axes determine the position of the point or object. A coordinate plane is formed by the intersection of two perpendicular lines called as x-axis and y-axis. It is a 2D plane. It is also called the cartesian coordinate system.

The cartesian coordinate system is of two types:

• Plane: Under this system, the line is not the limitation of the object. Anywhere on the plane, the position of the object can be elucidated by two upended numbers lines. i.e., x-axis and y-axis.
• Three-Dimensional: When three perpendicular number lines i.e. x-axis, y-axis, and z-axis specify the position of a point in the space.

#### Cartesian Plane & Coordinate Axes

When two intersecting lines describe the position of a point on the surface, it consists of two perpendicular lines and zero is the intersection point of both. This point is called the origin of the plane.

The horizontal line is the X – axis while the vertical line is the Y – axis; x is the horizontal distance of the point and, y is the vertical distance.

#### Cartesian Plane in One Dimension

In the one-dimensional Cartesian coordinate system, we have a straight line, the midpoint of which is considered the point of origin ‘O’. The line segment on the right is positive and the one on the left is negative. To determine the points in one dimension a line known as the number line is used.

#### Cartesian Plane in Two Dimensions

It is shown on the X – Y plane. They are called an ordered pair and are represented within parentheses. The perpendicular lines X and Y are respectively known as abscissa and ordinate.

#### Cartesian Plane in Three Dimensions

As compared to the normal Cartesian plane, the 3D Cartesian plane has an extra axis Z perpendicular to XY. The set of three points (x,y,z) denotes any point present on this plane.

#### Equation of a Line in Cartesian Plane

General Form It is given as Ax + By + C = 0.

• Slope intercept Form

Let the coordinate of a point be x, y through which a line passes, the slope of the line be m, and y – intercept be c. The equation will be: y = mx + c

• Intercept Form of a Line

Let the x-intercept and y-intercept of a line be a and b. The equation of a line will be: y = mx + c

When the plane splits into four parts by the X-axis and Y-Axis, then it is known as Quadrants geometry. It is signified as I, II, III, IV in a counter-clockwise direction. The axes in a plane are called Cartesian axes and the plane is known as the Cartesian plane.

Quadrants are characterized by the following signs:-

• Quadrant x > 0 , y > 0
• Quadrant x < 0 , y > 0
• Quadrant x < 0 , y < 0
• Quadrant x > 0 , y < 0

#### The Coordinate Plane

A coordinate plane is formed by the intersection of two perpendicular lines called as x-axis and y-axis. It is a 2D plane. This topic is crucial and asked in exams very frequently.

1. What is coordinate in geometry?

Answer: When the coordinate system is used in geometry, then it is called coordinate geometry. Under this system, to figure out the position of the points on a Euclidean space, one or more numbers are used.

2. How do you introduce coordinate geometry?

Answer:  When an ordered pair of numbers are used to describe the position of points on the plane. Coordinate geometry is really helpful in determining whether the line is parallel or perpendicular.

3. Who is the father of coordinate geometry?

Answer: A French mathematician, Rene Descartes, is the father of coordinate geometry.

4. What are the topics in coordinate geometry?

Answer: Following are the topics in coordinate geometry:-

• Distance Formula
• Section Formula
• Area of Triangle
• Equation of Straight Line
• Locus
• Conic Section
• Parabola
• Circle
• Ellipse

5. What are the formulas of coordinate geometry?

Answer: Distance Formula : √(x2 – x1)2 + (y2 – y1)2

Angle Formula : tan 0 = m1 – m2/ (1+m1 X m2)

Section Formula: When the ratio m:n is internal – (m X x2+n X x1/ m+n, m X y2 +n X y1/m+n)

When the ratio m:n is external – (m X x2-n X x1/ m-n, m X y2 -n X y1/m-n)

Coordinate plane geometry is a way of analyzing geometrical shapes. It is among the most scoring topics. There are various coordinate geometry formulas which you should comprehend properly. We help you understand coordinate geometry first, with in-depth concept notes and explanatory video on the MSVgo app. The MSVgo philosophy is to enable a core understanding of any concept. MSVgo app has a video library that explains concepts with examples or explanatory visualizations or animation. To learn more about it, check out the MSVgo app and their official site. Stay tuned with the MSVgo app and cheerful learning!

### High School Physics

• Alternating Current
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### High School Chemistry

• Acids, Bases and Salts
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• Strategies for Enhancement in Food Production
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• The Endocrine System
• The Fundamental Unit Of Life
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• Transport in Plants

### High School Math

• Algebra – Arithmatic Progressions
• Algebra – Complex Numbers and Quadratic Equations
• Algebra – Linear Inequalities
• Algebra – Pair of Linear Equations in Two Variables
• Algebra – Polynomials
• Algebra – Principle of Mathematical Induction
• Binomial Theorem
• Calculus – Applications of Derivatives
• Calculus – Applications of the Integrals
• Calculus – Continuity and Differentiability
• Calculus – Differential Equations
• Calculus – Integrals
• Geometry – Area
• Geometry – Circles
• Geometry – Conic Sections
• Geometry – Constructions
• Geometry – Introduction to Euclid’s Geometry
• Geometry – Three-dimensional Geometry
• Geometry – Lines and Angles
• Geometry – Straight Lines
• Geometry – Triangles
• Linear Programming
• Matrices and Determinants
• Mensuration – Areas
• Mensuration – Surface Areas and Volumes
• Number Systems
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• Permutations and Combinations
• Probability
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• Trignometry – Height and Distance
• Trignometry – Identities
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### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
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• Cell – Structure And Functions
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• Crop Production And Management
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• Elements and Compounds
• Fibre To Fabric
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• Force And Pressure
• Forests: Our Lifeline
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• Garbage In, Garbage Out
• Getting To Know Plants
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• Life Processes: Nutrition in Animals and Plants
• Materials: Metals And Non-Metals
• Matter and Its States
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• Micro Organisms: Friend And Foe
• Motion And Measurement Of Distances
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• Reaching The Age Of Adolescence
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• The Living Organisms And Their Surroundings
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• Transportation In Animals And Plants
• Universe
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• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
• Measurement
• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
• Patterns
• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time