CO-ORDINATE GEOMETRYIn this chapter we shall first define the coordinates of a point in a plane with reference to two mutually perpendicular lines in the same plane. We shall also learn about the plotting of points ofpoints on the plane (Cartesian plane) which will be used to draw the graphs of linear equations in one/two variables in the Cartesian plane.
HOW TO PLOT POINTS ON THE GRAPH? Take a graph paper. Draw two mutually perpendicular lines on the graph paper, one horizontal and other vertical. Might their intersection point as O (origin). The horizontal line as X’OX and the vertical line as Y’OY. The line X’OX is the x- axis and the line Y’OY as the y-axis. Choose a suitable scale on x-axis and y-axis and mark the points on both the axis. Obtain the coordinates of the point which is to be plotted. Let the point be P (a,b). To plot this point, start from the origin and move’│a│’ units along OX and OX’ according as ‘a’ is positive or negative. Suppose we arrive at point M. from point M move vertically upward or downward through │b │ units according as b is positive or negative. The point where we arrive finally is the required point P(a,b).
PLOTTING A POINT ON THE GRAPH(3,4) P (3,4)THUS POINT P REPRESENTS (3,4) ON THE GRAPH
PLOTTING A POING ON THE GRAPH (-4,2) N (-4,2)THUS POINT N REPRESENTS (-4,2) ON THE GRAPH
PLOTTING A POINT ON THE GRAPH (-2,-5) X (-2,-5)THUS POINT X REPRESENTS (-2,-5) ON THE GRAPH
PLOTTING A POINT ON THE GRAPH (2,-4) (2,-4) ZTHUS POINT Z REPRESENTS (2,-4) ON THE GRAPH
SUMMARY• In order to locate the position of a point in a plane we require two perpendicular lines. One of them is horizontal and another is vertical. The plane is called the Cartesian plane and the lines are known as the coordinate axes. The horizontal line is called the x-axis and the vertical line is known as the y-axis.• The coordinates axes divide the plane into four parts which are known as quadrants.• The point of intersection of the coordinate axes is called the origin.• The coordinates of the origin are (0,0)
• The distance of a point from x-axis is called its x- coordinate, or abscissa and the distance of the point from y-axis is called its y-coordinate or ordinate.• If x and y denote respectively the abscissa and ordinate of a point P, then (x,y) are called the coordinates of point P.• The y-coordinate of every point on y-axis is zero. So, the coordinates of any point on x-axis are of the form (x,0).• The x-coordinate of every point on x-axis is zero. So, the coordinates of any point on y-axis are of the form (0,y)
• The signs of coordinate (x,y)of a point in various quadrants are as given below – QUADRANT COORDINATES X y 1 + + 2 - + 3 - - 4 + -