Ordinate

Ordinate refers to the planar representation of a point in the cartesian coordinate system, and it is a term used to describe it. A point in a cartesian plane with the y coordinate of any point in the coordinate system is referred to as the ordinate. It refers to the distance between a point and the X-axis that is perpendicular to the Y-axis and parallel to the X-axis. The ordinate is a measure of the horizontal distance between a point and its origin. If two points have the same ordinate but different abscissa, then the line connecting the two points is a straight line parallel to the X-axis.

Cartesian coordinate system:

Rene Descartes, a great mathematician, was responsible for the development of the Cartesian coordinate system. It is used to represent the position of an object in space or on a plane, as well as the dimensions of the object. The cartesian plane is a two-dimensional representation of geometric figures that can be found in mathematics and geometry. The X and Y coordinates are used to represent the two dimensions of the object: length and width, respectively. In the same way, in cartesian space, the object is represented as a three-dimensional view of the world. These are the three dimensions of the object represented by the axes of the X, Y, and Z axes: length, breadth, and height, respectively. P denotes a point in a cartesian plane, and the letters P denote the coordinates of that point (x, y). In the same way, a point in cartesian space is represented by the letter P. (x, y, z).

Plotting ordinates in coordinate system:

The cartesian plane is comprised of two axes, X and Y, that are mutually perpendicular to one another and the origin. To put it another way, the cartesian plane is a representation of two number lines that are mutually perpendicular to one another. The perpendicular axes divide the plane into four equal parts, which are referred to as quadrants by mathematicians. 

The ordinate of a point in a coordinate system represents the perpendicular distance between a point and the X-axis. Specifically, the vertical distance between a point and the origin. Assuming that a point is denoted by A (x, y), it is plotted on a cartesian plane at an angle of x unit from the Y-axis and at an angle of y unit with respect to the Y-axis. 

If both x and y are positive, the point is in the first quadrant of the diagram. If x is negative and y is positive, it is in the second quadrant of the coordinate plane. If both x and y are negative, the point is in the third quadrant of the coordinate plane. If x is positive and y is negative, it is in the fourth quadrant. 

The ordinate in coordinate system example:

Locate and label the ordinate and abscissa of the points denoted by the letters A through E in the coordinate system example shown in Figure. Coordinate system example. In addition, specify which quadrant the point is located in.

Different forms of equation of a straight line:

An equation of a line can be expressed in a variety of ways. Some of them are explained in greater detail below: –

1] Equation for horizontal line: Parallel to the x-axis is a horizontal line drawn on the graph paper. As a result, all of the points on this line must be equally spaced apart from the x-axis. The distance between a point and the x-axis is defined by the ordinate. Because all of the points on a horizontal line are equally distant from the x-axis, the ordinates for all of the points on a horizontal line will be the same, i.e. y=k for all of the points on a given horizontal line.

2] Equation for vertical line: Parallel to the y-axis is a vertical line drawn vertically. As a result, all of the points along this line must be equally spaced from the y-axis. The distance between a point and the y-axis is defined by the abscissa. Given that all of the points on a vertical line are equally spaced apart from the y-axis, all of the points on a particular vertical line will have the same abscissa, which is x=k for all of the points on that vertical line.

3] Point slope equation: Point-slope equations can be used to solve for non-horizontal and nonvertical lines when we know the values of the slope and where a point on the line is located in relation to the line. We will treat the point I(x, y) as an imaginary point on this line, and the point P(x1, y1) as a defined point on this line. The point-slope equation can be represented as follows:

                m = (y−y1)/(x−x1)

                m(x-x1) = (y-y1) 

The line’s equation is obtained by plugging in the values of the slope and the defined point into an equation in terms of x and y, which is known as the slope-definition equation.

Conclusion:

In coordinate geometry, a straight line connecting any two points drawn parallel to one coordinate axis and meeting the other, particularly a coordinate measured parallel to the vertical. Ordinate refers to the planar representation of a point in the cartesian coordinate system, and it is a term used to describe it. A point in a cartesian plane with the y coordinate of any point in the coordinate system is referred to as the ordinate. 

The cartesian plane is a two-dimensional representation of geometric figures that can be found in mathematics and geometry.

The cartesian plane is comprised of two axes, X and Y, that are mutually perpendicular to one another and the origin. To put it another way, the cartesian plane is a representation of two number lines that are mutually perpendicular to one another.