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.The origin O is the point of intersection of the x-axis and the y-axis and has the coordinates (0, 0).The properties of the point represented in the four quadrants of the coordinate plane are: Further, any point in the coordinate plane is referred to by a point (x, y), where the x value is the position of the point with reference to the x-axis, and the y value is the position of the point with reference to the y-axis. These coordinate axes divide the plane into four quadrants, and the point of intersection of these axes is the origin (0, 0). The two axes of the coordinate plane are the horizontal x-axis and the vertical y-axis. It is also referred to as the coordinate plane. Coordinate PlaneĪ cartesian plane divides the plane space into two dimensions and is useful to easily locate the points. Here we shall try to know about the coordinate plane and the coordinates of a point, to gain an initial understanding of Analytical geometry. Analytical geometry is an important branch of math, which helps in presenting the geometric figures in a two-dimensional plane and to learn the properties of these figures.

Calculus 1 with analytic geometry