Coordinate geometry introduction | cartesian plane, X & Y-coordinate

In this article we will get an idea about initial understanding of Coordinate geometry concepts like cartesian plane, quadrants, X-coordinate (abscissa), Y-coordinate (ordinate) & how to plot the points on a co-ordinate plane.

Basic Concepts of Coordinate geometry

Coordinate geometry is one of the important concept in mathematics. Coordinate Geometry is one of the new branch of mathematics to representation of a point on a plane with idea of two references.

The concepts of Co-ordinate Geometry were developed by Rene Descartes (1596-1650). He is a French mathematician and philosopher and he is established an association between algebraic equations and geometric curves and figures.

In the above figure we draw a vertical number line and horizontal number line meeting at a point perpendicular to each other. The intersection point is denoted as origin.

The horizontal number line XX¹ is known as X-axis and the vertical number line YY¹ is known as Y-axis.

The point where XX¹ & YY¹ intersecting each other is called the origin, and is denoted by ‘O’.

In this plane the positive numbers lie on the directions OX is called the positive direction of the X-axis, similarly OY is the positive Y-axis respectively. Also the negative numbers lie on the directions OX¹ is called the negative directions of the X-axis, similarly OY ¹ is the negative Y-axis respectively.

The plane here is known as the cartesian plane or co-ordinate plane or XY-plane. The X & Y axes are known as coordinate axes.

The coordinate plane is divided into four parts by these coordinate axes. These four parts are called the quadrants and are denoted by Quadrant -1 (Q1), Quadrant -2(Q2), Quadrant -3(Q3) & Quadrant -4( Q4) in anti clockwise direction.

Coordinates of a Point ( or) Locating of coordinate points

A quadrant also defined as a part of a cartesian or coordinate plane obtained when the two axes intersect each other.

Quadrant -1 (Q1) : x > 0, y > 0 (+x, +y)

Quadrant -2 (Q2) : x < 0, y > 0 (- x, +y)

Quadrant -3 (Q3) : x < 0, y < 0 (-x, -y)

Quadrant -4 (Q4) : x > 0, y < 0 (+x, – y)

X coordinate – The X-coordinate of a point is the distance from origin to foot of perpendicular on X-axis. The x-coordinate is also known as the abscissa.

Y coordinate – The Y-coordinate of a point is the distance from origin to foot of perpendicular on Y-axis. The y-coordinate is also known as the ordinate.

In the coordinate system, origin as a reference point to locate other points in a plane.

A coordinate is states the locate a point in two-dimensional space. The coordinates of a point are shown as (x, y).

Coordinates of Origin: The point “O” lies on Y-axis. Its distance from Y-axis is zero. Hence its x-coordinate is
zero. Also it lies on X-axis. Its distance from X-axis is zero. Hence its y-coordinate is zero.

So the coordinates of the origin “O” are denoted as a (0,0).

The point “A” is at a distance of 4 units from Y-axis measured along positive point of X-axis from origin. The same point is at a distance of 3 units from X-axis measured along positive point of Y-axis from origin.

The x-coordinate (abscissa) of A is 4 & The y-coordinate (ordinate) of A is 3.

Hence the coordinates of A are (4,3)

The x-coordinate (abscissa) of B is -3 & The y-coordinate (ordinate) of B is 4.

Hence the coordinates of B are (-3,4)

The x-coordinate (abscissa) of C is -3 & The y-coordinate (ordinate) of C is -4.

Hence the coordinates of C are (-3,-4)

The x-coordinate (abscissa) of D is 3 & The y-coordinate (ordinate) of D is -2.

Hence the coordinates of D are (3, -2)

The point “E” is at a distance of +2 units from the Y-axis and at a distance zero from the X-axis. Therefore the x-coordinate of “E” is 2 and y-coordinate is 0.

Hence the coordinates of “E” are (2,0).

The point “F” is at a distance of -4 units from the X-axis and at a distance zero from the Y-axis. Therefore the x-coordinate of “F” is 0 and y-coordinate is -4.

Hence the coordinates of “F” are (0, -4)