Please make notes on the Coordinate Geometry of a line
Answers
Step-by-step explanation:
COORDINATE GEOMETRY OF A LINE:
There are three ways commonly used in coordinate geometry: Give the coordinates of any two points on the line. Give the coordinates of one point on the line, and the slope of the line. Give an equation that defines the line.
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Coordinate Geometry
Every place on this planet has coordinates that help us to locate it easily on the world map. The coordinate system of our earth is made up of imaginary lines called latitudes and longitudes. The zero degrees 'Greenwich Longitude' and the zero degrees 'Equator Latitude' are the starting lines of this coordinate system. Similarly locating the point in a plane or a piece of paper, we have the coordinate axes with the horizontal x-axis and the vertical y-axis.
Coordinate geometry is the study of geometric figures by plotting them in the coordinate axes. Figures such as straight lines, curves, circles, ellipse, hyperbola, polygons, can be easily drawn and presented to scale in the coordinate axes. Further coordinate geometry helps to work algebraically and study the properties of geometric figures with the help of the coordinate system.
What Is Coordinate Geometry?
Coordinate geometry is an important branch of math, which helps in presenting the geometric figures in a two-dimensional plane and to learn the properties of these figures. Here we shall try to know about the coordinate plane and the coordinates of a point, to gain an initial understanding of Coordinate geometry.
Coordinate Plane
A cartesian plane divides the plane space into two dimensions and is useful to easily locate the points. It is also referred to as the coordinate plane. The two axes of the coordinate plane are the horizontal x-axis and the vertical y-axis. These coordinate axes divide the plane into four quadrants, and the point of intersection of these axes is the origin (0, 0). Further, any point in the coordinate plane is referred to by a point (x, y), where the x value is the position of the point with reference to the x-axis, and the y value is the position of the point with reference to the y-axis.
The properties of the point represented in the four quadrants of the coordinate plane are:
The origin O is the point of intersection of the x-axis and the y-axis and has the coordinates (0, 0).
The x-axis to the right of the origin O is the positive x-axis and to the left of the origin, O is the negative x-axis. Also, the y-axis above the origin O is the positive y-axis, and below the origin O is the negative y-axis.
The point represented in the first quadrant (x, y) has both positive values and is plotted with reference to the positive x-axis and the positive y-axis.
The point represented in the second quadrant is (-x, y) is plotted with reference to the negative x-axis and positive y-axis.
The point represented in the third quadrant (-x, -y) is plotted with reference to the negative x-axis and negative y-axis.
The point represented in the fourth quadrant (x, -y) is plotted with reference to the positive x-axis and negative y-axis.
Coordinates of a Point
A coordinate is an address, which helps to locate a point in space. For a two-dimensional space, the coordinates of a point are (x, y). Here let us take note of these two important terms.
Abscissa: It is the x value in the point (x, y), and is the distance of this point along the x-axis, from the origin
Ordinate: It is the y value in the point (x, y)., and is the perpendicular distance of the point from the x-axis, which is parallel to the y-axis.
The coordinates of a point are useful to perform numerous operations of finding distance, midpoint, the slope of a line, equation of a line.
Topics Covered in Coordinate Geometry
The topics covered in coordinate geometry helps in the initial understanding of the concepts and formulas required for coordinate geometry. The topics covered in coordinate geometry are as follows.
About the Coordinate plane and the terms related to the coordinate plane.
Know about the coordinates of a point and how the point is written in different quadrants.
Formula to find the distance between two points in the coordinate plane.
The formula to find the slope of a line joining two points.
Mid-point Formula to find the midpoint of the line joining two points.
Section Formula to find the points dividing the join of two points in a ratio.
The centroid of a triangle with the given three points in the coordinate plane.
Area of a triangle having three vertices in the coordinate geometry plane
Equation of a line and the different forms of equations of a line
Coordinate Geometry Formulas
The formulas of coordinate geometry help in conveniently proving the various properties of lines and figures represented in the coordinate axes. The formulas of coordinate geometry are the distance formula, slope formula, midpoint formula, section formula, and the equation of a line. Let us know more about each of the formulas
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