Chapter 1 - Real Numbers. Chapter 2 - Polynomials. Chapter 4 - Quadratic Equations. Chapter 5 - Arithmetic Progressions.
Chapter 6 - Triangles. Chapter 7 - Coordinate Geometry. Chapter 8 - Introduction to Trigonometry. Chapter 9 - Some Applications of Trigonometry. Chapter 10 - Circles. Chapter 11 - Constructions. Chapter 12 - Areas Related to Circles. Chapter 13 - Surface Areas and Volumes. Chapter 14 - Statistics. Chapter 15 - Probability. Coordinate Geometry. Coordinate Geometry is the branch of Mathematics that helps us exactly locate a given point with the help of an ordered pair of numbers.
Coordinate geometry is also known as Cartesian Geometry. It helps you find the distance between two points whose coordinates are given. You can also find the coordinates of the point which divides the line segment joining two given points in the given ratio. Also you will learn how to find the area of a triangle in terms of the coordinate of its vertices. The five sections are introduction to coordinate geometry, formula to calculate distance between two pints, finding the coordinate of the point dividing the line in a particular ratio called section formula and finding the area of triangle in the form of coordinates of their vertices.
Exercise 7. It helps you to find the distance between any two points given on a plane. Section Formula deals with finding the coordinates of a point dividing the line in the particular ratio. What is Coordinate Geometry. We have studied number lines to mark any point. Descartes invented the idea of placing two perpendicular lines to each other on a plane, and locating points on the lines of the plane. The perpendicular lines may be in any direction but usually one line is horizontal and the other vertical.
Coordinate Geometry is the branch of mathematics that helps us to exactly locate a given point with the help of an ordered pair of numbers. Coordinate geometry is the combination of geometry and algebra to solve the problems. Coordinate geometry is also said to be the study of graphs. Graphs are visual representations of our data. It can be in different forms like bar graphs, histograms, line graphs, etc. Terms Related to Coordinate Geometry. While studying coordinate geometry the students must be aware of some important terms related to coordinate geometry they are well explained in this chapter.
From this figure, let us understand some important terms used in the coordinate formula of geometry. Axes of Coordinates. In the above figure OX and OY are called X-axis and Y-axis respectively and both together are known as axes of coordinates. The point of intersection of the axes is called the origin; it is O.
The distance of any point on the plane from the Y-axis is called the abscissa. The distance of any point on the plane from the X-axis is said to be ordinate. Coordinate of the Origin. It has zero distance from both the axes. Therefore the coordinates of the origin are 0, 0.
The axes Ncert Class 10th English First Flight Chapter 5 Read divide the plane into four parts. These four parts are said to be quadrants. The plane is called the coordinate plane or the XY-plane and the axes are called the coordinate axes. In the first quadrant, both the coordinates are positive. In the second quadrant, the y-coordinate is positive and x-coordinate is negative. In the third quadrant, both the coordinates are negative. In the fourth quadrant, the y-coordinate is negative and the x-coordinate is positive.
Distance Formula. In chapter 7 Maths Class 10 we learn about distance formulas for finding distance between two points. Finding the distance between the two points by using formula when the two coordinates of the points are given.
Section Formula. Section formula helps us in finding the coordinates of the point dividing the line in the ratio m:n. If P is the point dividing the line AB in the ratio m:n where coordinates of A x 1 , y 1 and B x 2 , y 10th Ncert Maths Chapters Reviews 2.
Area of Triangle. It will let us find the area of any triangle in terms of coordinates of its vertices. This formula will also be used in finding the area of quadrilaterals. All the basic formulas of coordinate geometry will help you to solve your geometry and algebra problems. Chapter 7 maths Class 10 provides you the list of all formulas of coordinate geometry to solve all the related problems. General Form of a Line.
Where A , B, C are real numbers and x and y are variables. Slope Intercept Form of a Line. Where x and y are variables, c is constant and m is the slope. Point-Slope Form. The slope of a Line Using Coordinates. The slope of a Line Using General Equation. Intercept-Intercept Form. Distance between two points O x 1, y 1 and B x 2, y 2. For Parallel Lines,. For Perpendicular Lines,. Angle between Two Lines.
Area of a Triangle. Perpendicular Distance from a Point to a Line. It is very important to get acquainted with these basic formulas of coordinate geometry. Chapter 7 Maths Class 10 coordinate formulas have been proven very helpful for students to solve the problems at a competitive level. Historical Facts. Rene Descartes, the Great French Mathematician of the seventeenth century, liked to lie in bed and think. One day, when lying in the bed he solved the problem of describing the position of a point in a plane.
His method was based on the old concept of latitude and longitude. Rene Descartes , a French Mathematician, came up with a system known as the cartesian coordinate system to describe the positions of points and lines in a plane. His latin name was Renatius Cartesius, hence the name cartesian plane was derived. He was referred to as the father of analytical geometry. Through cartesian coordinate or rectangular coordinate system, we can study the problems involving both geometry and algebra,.
Cartesian geometry is also termed as analytic geometry. Today it is strongly believed that success comes from regular practice. Intelligence also sometimes fails if not practiced. Maths needs a regular practice for perfection. Some people think Maths as a very tough subject, but if they have a regular practice of solving the problems they can crack any problem. Regular practice reduces the silly mistakes done during the examinations. Practising lots of problems makes you aware of all the possible questions related to any topic.
It makes it easier to solve any problem during your final exams. NCERT syllabus is designed according to the caliber of the students. Practicing NCERT problems after understanding the concept makes the students more confident in that area. Practicing not only improves your conceptual understanding but also improves your logical reasoning. Understanding the concept thoroughly and then solving the NCERT question will definitely increase your score in examinations.
Improves your accuracy.
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