Introduction
Cartesian System
Cartesian Planes and Coordinated axes
Quadrants
The Coordinate Planes
FAQs
Conclusion
Coordinate Geometry is one of the easiest topics in geometry. The topic deals with the link between geometry and algebra through lines and curves and is also known as analytic geometry. Coordinate geometry includes components like the x coordinates and y coordinates, which denotes points in a line. X coordinates indicate the distance between the point and the x axis, and the y coordinates represent the distance between the point and the y axis. This article explores the chapter on coordinate geometry in detail.
The Cartesian system explores the specification of every point distinctly in a plane set up by numerical coordinates. It contains two perpendicular lines, the same unit of length for both lines and orientation for both lines and has x, y, and z axes. The Cartesian system makes n number of coordinates in an n-dimensional Euclidean space. The point where both axes meet is known as the origin point of both the lines. Suppose the origin point of both lines is X. Then, any line drawn perpendicular to each axis through the point X and the position in which the line meets the axis represents a number. The axes' first and second coordinates are known as abscissa and ordinate, respectively. Among the two axes of the Cartesian system, the x axis is always horizontal and more inclined towards the right and the y axis is always vertical and more inclined towards the left. The Cartesian system of coordinate geometry has three-dimensional systems consisting of three lines with a common origin, that is, the lines intersect at the same point. These lines become perpendicular pairwise and are identical in length. Therefore, the Cartesian system is mainly of two types: a plane where the line does not limit the object and the three-dimensional system where three lines originate from the same point. They are perpendicular to each other and have the same lengths.
As discussed before, the origin point of the plane is the intersection between two perpendicular lines, which is also known as zero. Listed below are the three types of Cartesian planes:
Quadrants are the divisions between the X and Y axis planes. It is the meeting point of the X axis and Y axis. The meeting point of the two axes is 0,0. When they intersect with each other, these axes causes the plane to divide into four sections. Therefore, there are a total of four quadrants. Listed below are the four quadrants in coordinate geometry:
First Quadrant: The first quadrant is usually located in the upper right-hand corner of the plane. The numerical values in the first quadrant are always positive.
Second Quadrant: The second quadrant is usually situated in the upper left-hand corner of the plane. The numerical values in the second quadrants are always negative and positive. The Y values are positive, and the numerical values of the X axis are negative.
Third Quadrant: The third quadrant is usually located in the lower left-hand corner of the plane. The numerical values in the third quadrant are always negative. The numerical values of both X and Y are negative.
Fourth Quadrant: The fourth quadrant is usually situated on the lower right-hand side of the plane. The numerical values in the fourth quadrant are always positive and negative. The numerical values of X are positive, and the numerical values of Y are negative.
Quadrants generally determine the position of a particular point in the Cartesian planes.
The coordinate plane is also known as the Cartesian plane and rectangular coordinate plane grid. It is a two-dimensional plane consisting of two axes: the X axis and Y axis. The intersection of the X and Y axes forms the coordinate plane. The plane also consists of perpendicular lines that do not meet each other, resulting in not being able to view the whole coordinate plane in its entirety. However, since the lines intersecting have the same length, the planes are usually identical. The points at which the X and the Y axes intersect are the origin point. The numerical value of the origin is always 0, and the numerical values increase on the right side from the origin point of the plane and decrease and turn negative on the left side of the plane.
Coordinate plane graphs are planes with two number lines that run perpendicular and meet at the origin point, also known as zero. These number lines are known as the X axis and Y axis that are horizontal and vertical, respectively. Coordinate plane graphs are also known as coordinate planes. They are two-dimensional figures created by two axes intersecting each other.
The origin is the point of intersection between the X and Y axes. In other words, it is the starting point of the points. The numerical value of the origin point is always zero. The numerical values of the lines are determined through the value of the origin, that is, if the origin is zero, the right side of the origin point in the line will have positive values starting with plus (+) and the left side of the origin point in the numerical line will have negative values beginning with a minus (-). The origin point is present in all coordinate planes.
The Cartesian coordinate system has three dimensions. The first dimension is a one-dimensional figure with only one line and one origin point of the numerical value of 0. The second dimension is a two-dimensional figure that contains two lines intersecting each other. Both lines are perpendicular to each other and have the same length unit and orientation of each axis. The third dimension is a three-dimensional figure consisting of three perpendicular lines that intersect at a common point. Two of the three lines have identical units of length.
Abscissa and ordinate are present in the two-dimensional planes of the Cartesian coordinate system. The abscissa is the first coordinate of the plane. It refers to the horizontal axis, also known as the x axis. The distance of coordinates from the y axis is the absicca. The ordinates are the second coordinate of the plane. It refers to the vertical axis, also known as the y axis. The distance of coordinates from the x axis is known as the ordinate. The abssica and ordinate are perpendicular to each other. They meet and intersect at the point of origin where the numerical value is zero.
The first quadrant is located in the upper right-hand corner of the quadrant. The numerical values of the first quadrant are generally positive. The second quadrant is located in the upper left-hand corner of the quadrant. The numerical values of the second quadrant are positive and negative. The Y axis value is usually positive, and the X axis is generally negative. The third quadrant is located in the lower left-hand corner of the quadrant. The numerical values of the third quadrant are usually negative. The fourth quadrant is situated on the lower right-hand side of the quadrant. The numerical values are generally negative and positive. The Y axis values are negative here, and the X axis values are positive.
Coordinate geometry deals with various axes that help locate points in the planes and graphs. Studying this chapter at great lengths is vital as numerous questions come in the exams. In addition, coordinate planes are critical since many questions come from that particular topic. Therefore, students must study it with utmost concentration.
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