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Coordinate Axes
If a pair of perpendicular lines XOX dash and YOY dash intersect at O, these lines are called the coordinate axes.
The plane containing the axes is called the Cartesian Plane. The axes divide the cartesian plane into four quadrants.
The lines XOX dash and YOY dash are usually drawn horizontally and vertically as shown in the fig. and are known as x axis and y axis respectively.
The point of intersection of the axes i.e., the point O is called the Origin.
Values of x measured from O along the x - axis and are called abscissae. Along OX, x has positive values while along OX dash, x has negative values.
Similarly, the values of x measured from O along the y - axis and are called ordinates. Along OY, y has positive values while along OY dash, y has negative values.
The ordered pair containing the abscissa and the ordinate of a point is called the coordinates of the point.
Example If the abscissa of a point is 2 and the ordinate is 7, then the coordinates of the point are written as (2, 7).
Let us now see how to plot a point
Suppose P is any point in the plane. Draw Pl perpendicular to XOX dash and PM is perpendicular to YOY dash.
Let OL is equal to x and OM is equal to y.
Then, the ordered pair x, y is said to be define the point P. Also x and y are called cartesian coordinates of point P.
Thus we find to each point in the plane, we can associate an ordered pair x, y of real numbers.
Conversely, given any ordered pair of real numbers, we can plot the point in the plane. Click the button to view the example.
Plot the points having coordinates A (2, 4), B (-3, 4), C (4, -2), D(2, 0), E (0, 3) and F(-6, -4) on a graph paper mark the mutually perpendicular x and y axis and the origin O. Assume a suitable scale for each axis. Here we assume that 1cm on the x axis represents 2 units. Similarly, on the y axis1 cm represents 2 units .
We shall illustrate the method by plotting the point A (2, 4)
The abscissa is 2
Hence, draw a perpendicular to the x - axis at a point 2 units away from origin on the positive x - axis OX.
The ordinate of point A is 4
Hence, draw a perpendicular to the y - axis at a point 4 units away from origin O on the positive y - axis OY.
The point of intersection of these two lines is the required point A. In the same way the remaining points are plotted.
Observe the illustration
Coordinate Axes
If a pair of perpendicular lines XOX dash and YOY dash intersect at O, these lines are called the coordinate axes.
The plane containing the axes is called the Cartesian Plane. The axes divide the cartesian plane into four quadrants.
The lines XOX dash and YOY dash are usually drawn horizontally and vertically as shown in the fig. and are known as x axis and y axis respectively.
The point of intersection of the axes i.e., the point O is called the Origin.
Values of x measured from O along the x - axis and are called abscissae. Along OX, x has positive values while along OX dash, x has negative values.
Similarly, the values of x measured from O along the y - axis and are called ordinates. Along OY, y has positive values while along OY dash, y has negative values.
The ordered pair containing the abscissa and the ordinate of a point is called the coordinates of the point.
Example If the abscissa of a point is 2 and the ordinate is 7, then the coordinates of the point are written as (2, 7).
Let us now see how to plot a point
Suppose P is any point in the plane. Draw Pl perpendicular to XOX dash and PM is perpendicular to YOY dash.
Let OL is equal to x and OM is equal to y.
Then, the ordered pair x, y is said to be define the point P. Also x and y are called cartesian coordinates of point P.
Thus we find to each point in the plane, we can associate an ordered pair x, y of real numbers.
Conversely, given any ordered pair of real numbers, we can plot the point in the plane. Click the button to view the example.
Plot the points having coordinates A (2, 4), B (-3, 4), C (4, -2), D(2, 0), E (0, 3) and F(-6, -4) on a graph paper mark the mutually perpendicular x and y axis and the origin O. Assume a suitable scale for each axis. Here we assume that 1cm on the x axis represents 2 units. Similarly, on the y axis1 cm represents 2 units .
We shall illustrate the method by plotting the point A (2, 4)
The abscissa is 2
Hence, draw a perpendicular to the x - axis at a point 2 units away from origin on the positive x - axis OX.
The ordinate of point A is 4
Hence, draw a perpendicular to the y - axis at a point 4 units away from origin O on the positive y - axis OY.
The point of intersection of these two lines is the required point A. In the same way the remaining points are plotted.
Observe the illustration
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