What Are X and Y Coordinates?
Coordinates are a set of values that show the position of a certain point in a two-dimensional space. These positions are marked according to the numbers of the horizontal axis (x-axis) and the vertical axis (y-axis). The x and y coordinates of any given point have positive or negative values based on where the issue is in the different quadrants.
Coordinates can also be used to determine the specific position of more complex figures, including lines, circles, planes, or spheres.
A few key terms are important when working with x and y coordinates. These terms are:
Abscissa: The abscissa is the name given to the x value in the point. It is also the distance of this point along the x-axis from the origin.
The ordinate is the name given to the y value in the point. It is also the perpendicular distance of the end from the x-axis and the length of this same point along the y-axis from the origin.
X and Y Coordinates In Four Quadrants
Quadrant is the name given to the region enclosed by the intersection of the x-axis and the y-axis. When the x-axis and the y-axis intersect with one another at 90º, four areas are formed around it. These regions are called quadrants. Every plane has four quadrants, each of which is bounded by half of the axes. The quadrants are named Quadrant I, Quadrant II, Quadrant III, and Quadrant IV based on their position on the axes.
The four quadrants are as follows:
- The first quadrant is on the upper right-hand corner of the plane. In this quadrant, the x and y-coordinates are both positive.
- The second quadrant is on the upper left-hand corner of the plane. In this quadrant, the x-coordinate is negative, while the y-coordinate is positive.
- The third quadrant is on the lower left-hand corner of the plane. In this quadrant, the x and y-coordinates are both negative.
- The fourth quadrant is on the lower right-hand corner of the plane. In this quadrant, the x-coordinate is positive, while the y-coordinate is negative.
How To Work Out Coordinates
To read coordinates, we need to understand how to write them. A point on a grid contains two numbers to let us know a position. These numbers are the coordinates. They are provided by first giving the number of steps across (x-axis) followed by the steps up or down (y-axis).
So, to locate the treasure on the map below, we must know the coordinates, which are G,4. Therefore, if you are positioned in the same spot as the mermaid, you will need to move six steps along the x-axis to G,4.
If you are currently positioned on the pirate ship, you need to move two steps along the x-axis to G, then three up the y-Axis to 4. Then, bingo! You’ve found the treasure.
Uses of X and Y Coordinates
A question often arises in maths lessons: How is this information useful? Well, x and y coordinates are one of the many mathematics areas with many practical, real-life applications. For instance, the x and y coordinates of a point can be used to perform the following actions:
- The x and y coordinates can assist us in finding a point in the coordinate axes.
- The x and y coordinates for two points can be used to find the distance between the two points.
- The x and y coordinates for two points help find the slope of a line.
- The x and y coordinates for two points help find the equation of a line.
Who Invented Coordinates?
The coordinate system we use is the Cartesian System, also called the Plane System. It’s named after French mathematician René Descartes, who designed it in the 17th century. René Descartes published his ideas surrounding coordinates in 1637. A fellow mathematician called Pierre de Fermat, whose field of work was also in three dimensions, had made similar discoveries about coordinates. However, Fermat did not publish his discovery.
According to legend, Descartes discovered the Cartesian system after watching a fly from the ceiling of his bed and wondered how he could point out its location. He used the corner of the top as a reference point and created a link between algebra and geometry that changed how maths would be seen forever.
Various other coordinate systems have been developed since René Descartes’ original discoveries. These systems include the polar coordinates for the plane and the spherical and cylindrical coordinates for three-dimensional space.