# Chapter 7 – 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 common topics in mathematics that you might have come across. Coordinate geometry explains the link between geometry and algebra through curves and lines. An ordered pair of numbers is used to describe the position of points on the plane. Coordinate geometry is also called analytic geometry. 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 to help you understand the basics without any issues.

#### Cartesian System

The Cartesian system is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. For a three-dimensional system, we have three axes, i.e., x, y, and z. It is used to make n coordinates for any point in n-dimensional Euclidean space.

The cartesian coordinate system is of two types:

• Plane: Under this system, the line is not the limitation of the object.
• Three-Dimensional: When three perpendicular number lines, i.e., x-axis, y-axis, and z-axis, specify the position of a point from a certain reference point in the space.

#### Cartesian Plane & Coordinate Axes

When two intersecting lines explain 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.

A Cartesian plane has two directed lines that intersect at zero. The horizontal line is called the x-axis, and the vertical line is known as the y-axis.

The Cartesian plane consists of:-

• One-Dimensional Cartesian Plane

To make a one-dimensional plane, you have to draw a straight line and choose a point o as the origin. The o should be in the middle. On the right side, the line segment is positive, and the left would be negative—accordingly, use + and – sign. A line known as the number line is used to determine the points in one dimension.

• Two-Dimensional Cartesian Plane

The two-dimensional plane is shown by x and y. These perpendicular lines X and Y are called abscissa and ordinate. It has two perpendicular lines. The point at which both the axes meet is 0.

• Three-Dimensional Cartesian Plane

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 from a certain reference point present on this plane.

When the plane splits into four parts by the X-axis and Y-Axis, it is known as Quadrants geometry. It is shown through numerical numbers as I, II, III, IV.

• 1st Quadrant: The first quadrant is at the upper right-hand corner of the graph. In this, all the values are positive.
• 2nd Quadrant: The second quadrant is at the upper left-hand corner of the graph. The value of y is positive, and the value of x is negative.
• 3rd Quadrant: The third quadrant is at the lower left-hand corner of the graph. Both x and y values are negative.
• 4th Quadrant: The fourth quadrant is the lower right-hand corner having positive values of x and negative values of y.

Quadrants are shown 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

It is flat, having a two-dimensional surface that lengthens infinitely far. It is formed by the intersection of two perpendicular lines called as x-axis and y-axis. A coordinate plane cannot be viewed completely. They are usually parallel to each other and tend to be identical. The coordinate plane questions are asked very frequently in examinations; thus, making it very important from your exams’ point of view.

#### FAQs

What is the formula of coordinate geometry?

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

Angle Formula : tan 0 = m1 – m2/ 1+m1m2

Section Formula: When the ratio m:n is internal – (mx2+nx1/ m+n, my2 +ny1/m+n)

When the ratio m:n is external – (mx2-nx1/ m-n, my2 -ny1/m-n)

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 points on a Euclidean space, one or more numbers are used.

Why is coordinate geometry important?

Answer. It is important because of the following reasons:

It provides a relationship between algebra and geometry with the help of graphs and curves.

It assists in solving geometric problems algebraically.

What are the four parts of a coordinate plane?

Answer. The coordinate plane is divided into four sections by the intersecting of x and y axes. These four sections are known as quadrants.

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

Coordinate geometry is among the simplest topics in mathematics. There are various coordinate geometry formulae that you should comprehend properly. We help you understand coordinate geometry basics 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, 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 enjoy learning!

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### High School Math

• Algebra – Arithmatic Progressions
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### Middle School Math

• Area and Its Boundary
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