Today, in many of the exact sciences, people use the coordinate plane. Even at school, we built various graphs with these coordinates and solved examples. So what is a coordinate plane?
A coordinate plane is a two-dimensional system formed by two lines (horizontal and vertical). As a rule, these lines have a well-established designation. The vertical line is called the y-axis, and the horizontal line is called the x-axis. There is also a coordinate origin in such a plane. It is the point of intersection of the lines (0;0). At the intersection, the coordinates form the so-called four quadrants. There are two minus planes. It is the left part on the x-axis and the lower part on the y-axis. The other two are positive.
The coordinate system is a brilliant invention of the human mind. The beginning was laid by the scientist Hipparchus, who proposed to enter the geographical coordinates. In the 17th century, the French mathematician Rene Descartes systematized scientific knowledge and became the founder of the currently most famous and used coordinate system. He made the first scientific description of the rectangular coordinate system in 1637. Therefore, this rectangular coordinate system is called a Cartesian system.
Also, Pierre Fermat made a significant contribution to the development of the coordinate plane. Descartes and Fermat used the coordinate method only on the plane. And in the next century, this system was applied in three-dimensional space by Leonhard Euler. But for now, talk about the usual one you can draw on online graph paper.
To determine the coordinates, people everywhere use symbols. The x-coordinate or abscissa point is the distance from the y-axis along the x-axis. The same applies to the y-coordinate or the ordinate. If you want to plot a graph, first use x-coordinate and y-coordinate. Usually, this data is placed in parentheses (x;y). Thanks to this plane, you may solve algebraic problems and graphs. It visualizes and simplifies the understanding of the work. There are also signs of the numbers to understand distances. Thanks to them, you may determine the final number of a mathematical problem.
Now talk about determining the coordinates in practice. To find the location of a particular point, start from the origin (0;0). For instance, you have the coordinates (5;-2). Move to the right on the x-axis to the number five. It is the first ordered number. Next, from the number five, move down two digits on the y-axis. It should coincide with the coordinate of the abscissa. This ordinate is the second number in the ordered pair. Thus, when constructing, you get the point (5;-2). There is nothing complicated. The main thing is to be careful. By the way, when creating a graph, be sure to mark all the points found with coordinates. It is a prerequisite in mathematical construction.
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As noted earlier, using the coordinate plane and the main points, you may make a graph of the function and solve mathematical equations. To do this, you must have known the coordinates. Suppose there are two of them (4; 6) and (-3;-5). Follow the steps of making the graph, and you will succeed:
By the way, such a function is called linear. It is the simplest function of all other algebraic ones. For instance, the most commonly used one is the quadratic function, and its graph is called a parabola. There is also a power function. In a linear system, x-coordinate is an independent variable, but y-coordinate is a dependent one. It is usually denoted as follows: y = kx+m, where (k) and (m) are some numbers. In general, nothing complicated! Try to remember the foundation of these graphs and their designations.
Coordinate systems permeate the entire practical life of a person. In our speech, you may have heard this phrase more than once: “Give me your coordinates.” What does this expression mean? The interlocutor asks you to write down your address or phone number. Each person has situations when it is necessary to determine the location.
Coordinates surround us everywhere:
In general, the scope of this universal system is diverse. Thus, the coordinate plane is not difficult to understand. This convenient system allows you to navigate the terrain and solve many mathematical tasks.