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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 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 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 Ch 3 Maths Class 10 Pdf Github 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.
From the Class 10 board point of view, the entire function chapter is extremely important. The questions are based on concepts like the distance between the two points whose coordinates are given, to find the area of the triangle formed by three given points, how to find the coordinates of the point which divides a line segment joining two given points in a given ratio.
Deep understanding of function on one side will help you to score more in your coming exams and on the other side will lay a solid foundation for your further studies in Engineering and Science Research.
To conclude, Coordinate Geometry consists of a total of four exercises. In this chapter, you will also learn how to find the distance between two points whose coordinates are given and how to find the area of the triangle formed by three given points. Working on these sample questions will definitely help students to secure good marks in the exam.
Using distance formula, find which of them is correct. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.
Find the point on the x-axis which is equidistant from 2, -5 and -2, 9. Find the values of y for which the distance between the points P 2, -3 and Q 10, y is 10 units. If Q 0, 1 is equidistant from P 5, -3 , and R x, 6 , find the values of x.
Also, find the distances QR and PR. Find a relation between x and y such that the point x, y is equidistant from the points 3, 6 and -3, 4. The Perpendicular distance of x a point from the y-axis is called its x-coordinate or abscissa. The perpendicular distance y of a point from the x-axis is called its y-coordinate or ordinate.
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