origin of X axis lies on the right side
Answers
Answer:
Step-by-step explanation:
Whenever we are given a point in a plane we can associate with it an ordered pair of real numbers. This is done in the following way. In the plane, draw a real number line horizontally and a real number line vertically (with increasing values upward) so that the 0's on each line intersect. The horizontal real line is called the x-axis, the vertical real line is referred to as the y-axis and the point of intersection is called the origin.
We now construct perpendicular lines from the point to each of the axes. Suppose the perpendicular line to the x-axis meets at the real number u and the perpendicular line to the y-axis intersects at the real number v then we associate with the point the ordered pair (u,v). Conversely, any ordered pair of real numbers corresponds to a point in the plane. The ordered pair corresponding to a given point are called the coordinates of the point. Given the coordinates (u,v) of a point, we call the first number, u, the x-coordinate of the point and the second number, v, the y-coordinate of the point. When we introduce perpendicular axes into this plane in this way, we have a Cartesian coordinate plane (or just coordinate plane).
Notice that the coordinate axes (the collective name for the x- and y-axes) divide up the plane into 4 parts; these parts are called quadrants. We number them counter-clockwise, beginning from the quadrant in which both the x and the y-coordinates are positive. So they are:
Quadrant Number x-coordinate y-coordinate
First quadrant positive positive
Second quadrant negative positive
Third quadrant negative negative
Fourth quadrant positive negative
Note that points that lie on an axis do not lie in any quadrant. If a point lies on the x-axis then its y-coordinate is 0. Similarly, a point on the y-axis has its x-coordinate 0. The origin has coordinates (0,0).
On the right you see an example of a (Cartesian) coordinate plane with some points sketched in it.
Coordinates: Point A has x-coordinate 2 and y-coordinate 3, so we say it has coordinates (2,3). Point B has x-coordinate 1 and y-coordinate -2, so we say it has coordinates (1,-2).
Quadrants: Point A is in the first quadrant, and point B is in the fourth quadrant.
In the demonstration we have drawn a pair of axes in the plane. Move the mouse over the plane and you will be given the coordinates and the quadrant in which you are located.
If you click the mouse the demonstration will "freeze" and you will be shown the perpendicular lines from the point to the axes. Click the mouse a second time to reactivate the demonstration.
Cartesian Plane
Now if we are given the coordinates of a point, we may place this point in the plane geometrically. This is called plotting the point. You will practice plotting points and translating geometric representation of a point on a plane to its x and y-coordinates in the next activity.
True.................