##### 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.

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.

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.

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.

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*.

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.

**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

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!