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Complete Details Of CBSE Class 11 Commerce Maths Co-Ordinate Geometry

Complete Details Of CBSE Class 11 Commerce Maths Co-Ordinate Geometry

CBSE Class 11 Commerce Maths Co-Ordinate Geometry : The CBSE envisions a robust, vibrant and holistic school education that will engender excellence in every sphere of human endeavor. The Board is committed to provide quality education to promote intellectual, social and cultural vivacity among its learners. It works towards evolving a learning process and environment, which empowers the future citizens to become global leaders in the emerging knowledge society. The Board advocates Continuous and Comprehensive Evaluation with an emphasis on holistic development of learners. The Board commits itself to providing a stress-free learning environment that will develop competent, confident and enterprising citizens who will promote harmony and peace.

Complete Details Of CBSE Class 11 Commerce Maths Co-Ordinate Geometry

CBSE Class 11 Commerce Maths Co-Ordinate Geometry : Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.

Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Complete Details Of CBSE Class 11 Commerce Maths Co-Ordinate Geometry CBSE Class 11 Commerce Maths Co-Ordinate Geometry :  In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.

Analytic geometry is widely used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.

Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space (three dimensions). As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes’ numerical definitions and representations. The numerical output, however, might also be a vector or a shape. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.

1. Straight Lines

Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line.

2. Conic Sections

Sections of a cone: circles, ellipse, parabola, hyperbola; a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

3. Introduction to Three–dimensional Geometry

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.

Download here CBSE Class 11 Commerce Maths Co-Ordinate Geometry notes 

Complete Details Of CBSE Class 11 Commerce Maths Co-Ordinate Geometry

CBSE Class 11 Commerce Maths Co-Ordinate Geometry :   You have already studied how to locate a point on a number line. You also know how to describe the position of a point on the line. There are many other situations, in which to find a point we are required to describe its position with reference to more than one line. For example, consider the following situations: I. In Fig. 3.1, there is a main road running in the East-West direction and streets with numbering from West to East. Also, on each street, house numbers are marked. To look for a friend’s house here, is it enough to know only one reference point? For instance, if we only know that she lives on Street 2, will we be able to find her house easily? Not as easily as when we know two pieces of information about it, namely, the number of the street on which it is situated, and the house number. If we want to reach the house which is situated in the 2nd street and has the number 5, first of all we would identify the 2nd street and then the house numbered 5 on it. In Fig. 3.1, H shows the location of the house. Similarly, P shows the location of the house corresponding to Street number 7 and House number 4.

Summary In this chapter, you have studied the following points :

1. To locate the position of an object or a point in a plane, we require two perpendicular lines. One of them is horizontal, and the other is vertical.

2. The plane is called the Cartesian, or coordinate plane and the lines are called the coordinate axes.

3. The horizontal line is called the x -axis, and the vertical line is called the y – axis.

4. The coordinate axes divide the plane into four parts called quadrants.

5. The point of intersection of the axes is called the origin.

6. The distance of a point from the y – axis is called its x-coordinate, or abscissa, and the distance of the point from the x-axis is called its y-coordinate, or ordinate.

7. If the abscissa of a point is x and the ordinate is y, then (x, y) are called the coordinates of the point.

8. The coordinates of a point on the x-axis are of the form (x, 0) and that of the point on the y-axis are (0, y).

9. The coordinates of the origin are (0, 0).

10. The coordinates of a point are of the form (+ , +) in the first quadrant, (–, +) in the second quadrant, (–, –) in the third quadrant and (+, –) in the fourth quadrant, where + denotes a positive real number and – denotes a negative real number.

11. If x ≠ y, then (x, y) ≠ (y, x), and (x, y) = (y, x), if x = y.

Related Topics:

In these lessons, we will learn
  • the coordinate plane or Cartesian plane
  • the slope formula
  • the equation of a line
  • the slopes of parallel lines
  • the slopes of perpendicular lines
  • the midpoint formula
  • the distance formula
Coordinate Geometry Formulas

The following table gives some coordinate geometry formulas. Scroll down the page if you need more explanations about the formulas, how to use the formulas and worksheets to practice.

coordinate geometry formulas

What is a Coordinate Plane or Cartesian Plane?

The coordinate plane or Cartesian plane is a basic concept for coordinate geometry. It describes a two-dimensional plane in terms of two perpendicular axes: x and y. The x-axis indicates the horizontal direction while the y-axis indicates the vertical direction of the plane. In the coordinate plane, points are indicated by their positions along the x and y-axes.

For example: In the coordinate plane below, point L is represented by the coordinates (–3, 1.5) because it is positioned on –3 along the x-axis and on 1.5 along the y-axis. Similarly, you can figure out the positions for the points M = (2, 1.5) and N = (–2, –3).
coordinate plane

How to plot points in the coordinate plane and how to determine the coordinates of points on the coordinate plane?

To graph or plot points, we use two perpendicular lines called axes. The point at which the axes cross is called the origin. Arrows in the axes indicate the positive directions.
Consider the ordered pair (4, 3). The numbers in an ordered pair are called the coordinates. The first coordinate or x-coordinate in this case is 4 and the second coordinate or y-coordinate is 3.
To plot the point (4, 3) we start at the origin, move horizontally to the right 4 units, move up vertically 3 units, and then make a point.
Example:
1. Plot the following points: A(-3,2), B(-1,4), C(-2,-4), D(0,-2), E(3,0)
2. Find the coordinates of the given points
How to find the slope of a line?

On the coordinate plane, the slant of a line is called the slope. Slope is the ratio of the change in the y-value over the change in the x-value, also called rise over run.Given any two points on a line, you can calculate the slope of the line by using this formula:

slope =

For example: Given two points, P = (0, –1) and Q = (4,1), on the line we can calculate the slope of the line.

slope = = slope values

coord plane: slope

What is the Y-intercept?The y-intercept is where the line intercepts (meets) the y-axis.

For example: In the above diagram, the line intercepts the y-axis at (0,–1). Its y-intercept is equals to –1.

What is the Equation of a Line?

In coordinate geometry, the equation of a line can be written in the form, y = mx + b, where m is the slope and b is the y-intercept. (see a mnemonic for this formula)
equation of a line
For example: The equation of the line in the above diagram is: y=1/2x-1

Complete Details Of CBSE Class 11 Commerce Maths Co-Ordinate Geometry

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