Cartesian Coordinate System: Algebraic Equations
Cartesian Coordinate System
-A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Cartesian coordinate system is a way of locating objects in either two- or three-dimensional space by specifying their X(horizontal) position, Y (vertical) position and Z (through) position. It is used in graphics and in positioning text on documents.
-Algebraic equations involving the coordinates of the points lying on the shape. For example, a circle o f radius 2 may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.
A system …show more content…
or two or three mutually perpendicular axes along which any point can be precisely located with reference to any other point, often referred to as x, y and z coordinates. Relative measure of distance, area and direction are constant throughout the system. The Cartesian coordinate system is named after René Descartes.
The idea of this system was developed in 1637 in two writings by Descartes and independently by Pierre de Fermat, although Fermat used three dimensions, and did not publish the discovery. Two dimensions
In two dimensions the position of a point P in a plane can be specified by it's distance from two lines intersecting at right angles, called axes.
For instance, in Figure 1 two lines intersect each other at right angles in the point 0, the origin. One axis is the line O-X, the other O-Y and any point in the plane can be denoted by two numbers giving it's perpendicular distances from O-X and from O-Y.
A general point P can reached by traveling a distance x along a line O-X, and then a distance y along a line parallel to O-Y. O-X is called the x-axis, O-Y the y-axis, and the point P is said to have Cartesian coordinates (x, y). In the coordinate system shown, as is indicated in the diagram, the x-coordinate is positive for points above the right of the y-axis and negative for points to the left of this axis. The y-coordinate is positive for points above the x- axis and negative points below it. The coordinates of the origin are (0, …show more content…
0) Three dimensions
Three (black) lines, labeled X, Y, Z, are shown in three-dimensional Euclidean space.
They intersect in a point O, again called origin. The lines are x-, y-, and z-axis. As in two-dimensional case, the axes consist of two half-lines: a positive and a negative part of the axis. The frame is right handed, if we rotate the positive x-axis to the positive y-axis the rotation direction (by the corkscrew rule) is the direction of the positive z-axis. In older literature ans\d some special application one may find a left-handed Cartesian set of axes, in which the x- and the y-axis are interchanged.
Generalization
One can generalize the concept of Cartesian coordinates to allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). In those oblique coordinate systems the computations of distances and angles is more complicated than in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not
hold.
-Cartesian coordinate system allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis ,
Reflection in our daily life
-In the Cartesian coordinate system, the y-axis is the horizontal line of the reference, example is frame of reference in all sciences—and indeed, in our daily life.
MEMBERS:
Manayaga, Merry Christ
Guadamor, Paul Marion
Corsame, Pamela Gaile
-A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Cartesian coordinate system is a way of locating objects in either two- or three-dimensional space by specifying their X(horizontal) position, Y (vertical) position and Z (through) position. It is used in graphics and in positioning text on documents.
-Algebraic equations involving the coordinates of the points lying on the shape. For example, a circle o f radius 2 may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.
A system …show more content…
or two or three mutually perpendicular axes along which any point can be precisely located with reference to any other point, often referred to as x, y and z coordinates. Relative measure of distance, area and direction are constant throughout the system. The Cartesian coordinate system is named after René Descartes.
The idea of this system was developed in 1637 in two writings by Descartes and independently by Pierre de Fermat, although Fermat used three dimensions, and did not publish the discovery. Two dimensions
In two dimensions the position of a point P in a plane can be specified by it's distance from two lines intersecting at right angles, called axes.
For instance, in Figure 1 two lines intersect each other at right angles in the point 0, the origin. One axis is the line O-X, the other O-Y and any point in the plane can be denoted by two numbers giving it's perpendicular distances from O-X and from O-Y.
A general point P can reached by traveling a distance x along a line O-X, and then a distance y along a line parallel to O-Y. O-X is called the x-axis, O-Y the y-axis, and the point P is said to have Cartesian coordinates (x, y). In the coordinate system shown, as is indicated in the diagram, the x-coordinate is positive for points above the right of the y-axis and negative for points to the left of this axis. The y-coordinate is positive for points above the x- axis and negative points below it. The coordinates of the origin are (0, …show more content…
0) Three dimensions
Three (black) lines, labeled X, Y, Z, are shown in three-dimensional Euclidean space.
They intersect in a point O, again called origin. The lines are x-, y-, and z-axis. As in two-dimensional case, the axes consist of two half-lines: a positive and a negative part of the axis. The frame is right handed, if we rotate the positive x-axis to the positive y-axis the rotation direction (by the corkscrew rule) is the direction of the positive z-axis. In older literature ans\d some special application one may find a left-handed Cartesian set of axes, in which the x- and the y-axis are interchanged.
Generalization
One can generalize the concept of Cartesian coordinates to allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). In those oblique coordinate systems the computations of distances and angles is more complicated than in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not
hold.
-Cartesian coordinate system allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis ,
Reflection in our daily life
-In the Cartesian coordinate system, the y-axis is the horizontal line of the reference, example is frame of reference in all sciences—and indeed, in our daily life.
MEMBERS:
Manayaga, Merry Christ
Guadamor, Paul Marion
Corsame, Pamela Gaile