The coordinate axes ox and oy are rotated by an angle θ in the anti-clockwise direction, to obtain the new axes ox' and oy'. Any equation of a line or a curve with respect to the old axes, can be easily changed with reference to the new axes by simply replacing (x, y), in the equation with (x + h, y + k). The coordinates of a point transforms from (x, y) to (x' + h, y' + k). The new coordinate axes is translated such that the new axes are parallel to the old axes. Here we transfer the origin to a new origin O' located at the point (h, k) with respect to the old coordinate axes. The given coordinate axes with the origin as O has the coordinates of a point as (x, y). Let us know more about the translation and rotation of axes in the below sentences. Also the coordinates axes can also be rotated at an angle about the origin, with respect to the x-axis. The coordinate axes in analytical geometry can be translated by moving the axes such that the new axes are parallel to the old axes. The coordinates of a point are useful to perform numerous operations of finding distance, midpoint, the slope of a line, equation of a line.Īnalytical Geometry - Translation and Rotation of Axes Ordinate: It is the y value in the point (x, y)., and it is the perpendicular distance of the point from the x-axis, which is parallel to the y-axis.Abscissa: It is the x value in the point (x, y), and it is the distance of this point along the x-axis, from the origin.Here let us take note of these two important terms. For a two-dimensional space, the coordinates of a point are (x, y). The point represented in the fourth quadrant (x, -y) is plotted with reference to the positive x-axis and negative y-axis.Ī coordinates is an address, which helps to locate a point in space.The point represented in the third quadrant (-x, -y) is plotted with reference to the negative x-axis and negative y-axis.The point represented in the second quadrant is (-x, y) is plotted with reference to the negative x-axis and positive y-axis.The point represented in the first quadrant (x, y) has both positive values and is plotted with reference to the positive x-axis and the positive y-axis.Also, the y-axis above the origin O is the positive y-axis, and below the origin O is the negative y-axis. The x-axis to the right of the origin O is the positive x-axis and to the left of the origin, O is the negative x-axis.
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