Look at each quadrant in the graph below. What do you notice about the signs of the x- and y- coordinates of the points within each quadrant? Within each quadrant, the signs of the x- coordinates and y- coordinates of each ordered pair are the same. They also follow a pattern, which is outlined in the table below. General Form of Point in this Quadrant. Starting from the origin, go along the x- axis in a positive direction right and along the y- axis in a positive direction up.
Starting from the origin, go along the x- axis in a negative direction left and along the y- axis in a positive direction up. Starting from the origin, go along the x- axis in a negative direction left and along the y- axis in a negative direction down. Starting from the origin, go along the x- axis in a positive direction right and along the y- axis in a negative direction down. Once you know about the quadrants in the coordinate plane, you can determine the quadrant of an ordered pair without even graphing it by looking at the chart above.
The example below details how to determine the quadrant location of a point just by thinking about the signs of its coordinates. Thinking about the quadrant location before plotting a point can help you prevent a mistake. It is also useful knowledge for checking that you have plotted a point correctly. Look at the signs of the x- and y- coordinates. What happens if an ordered pair has an x- or y- coordinate of zero?
The example below shows the graph of the ordered pair 0, 4. A point located on one of the axes is not considered to be in a quadrant. It is simply on one of the axes. Whenever the x- coordinate is 0, the point is located on the y- axis. Similarly, any point that has a y- coordinate of 0 will be located on the x- axis. Which of the descriptions below best describes the location of the point 8, 0?
B It is on the x- axis. C It is on the y- axis. A Quadrant I. The axes are not considered part of the quadrant. Rather, they are the boundaries that define the quadrant. The correct answer is the x- axis. Adding and subtracting are very easy with Roman numerals. Indo-Arabic numerals can more easily be mistaken or forged — a 0 can look very like a 6 or an 8 or a 9 or be turned into one by a single stroke. The coordinate axes divide the plane into four quadrants, labelled first, second, third and fourth as shown.
By considering the x- and y-coordinates of the point P as it lies in each of the four quadrants, we can identify the sign of each of the trigonometric ratios in a given quadrant. It can also be defined as the 0,0 point in the coordinate plane. If x is negative and y is positive, then the point lies in the second quadrant. Note that the point 3,2 is not the same as point 2,3. The numbers in an ordered pair are called coordinates. The most common numbers that we encounter —in everything from speed limits to serial numbers—are natural numbers.
These are the counting numbers that start with 1, 2, and 3, and go on forever. If we start counting from 0 instead, the set of numbers are instead called whole numbers. The integer numbers or simply integers extend whole numbers to their opposites Notice that 0 is the only number whose opposite is itself. However, humans have long had some conception of negative numbers, due to phenomena such as measuring sea level or debt. Notice how mathematics rarely presents just one model for the real world.
Representing the concept of being opposite using a negative sign lets us represent all the integers on a number line that extends both to the left and to the right of zero. The positive integers are represented to the right of 0 and the negative integers are represented to the left of 0.
Coordinate graphing is a visual method for showing relationships between numbers. The relationships are shown on a coordinate plane. A coordinate plane has two perpendicular lines, or axes pronounced AK-seez , labeled just like number lines. With the extension of the number system to include negative numbers, each axis can be extended in two directions.
The horizontal axis is usually called the x -axis. The vertical axis is usually called the y -axis. The point where the x - and y -axis intersect is called the origin. The numbers on a coordinate plane are used to locate points.
Each point can be identified by an ordered pair of numbers; that is, a number on the x -axis called an x -coordinate , and a number on the y -axis called a y -coordinate. Thank you! Ultimately it's just a convention, and it could equally well have been different. But there are some other conventions it ought to align with so they would possibly also have to change to make everything fit together :.
As Yagna Patel points out, quadrant numbering is intimately connected with the standard parameterization of the unit circle. Change one and you'll have to change the other to fit if you don't want to go crazy. The horizontal axis could be either the first or second coordinate in a coordinate pair -- but it should grow from left to right because that is the reading direction in the language the trendsetting mathematicians communicate in.
Finally, we can number the quadrants either 1,2,3,4 or 0,1,2,3 without much influence on other conventions. It's a minor nuisance that these conventions are different, but neither is realistically changeable. My understanding is that the quadrants are numbered in the order an angle in standard position passes through them as the angle increases - that is, counterclockwise starting at the x axis.
Sign up to join this community.
0コメント