MathSteps: Grade 4: Coordinate Graphing: What Is It?
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a . The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. If the coordinates of a point are (x, y), then its distances from the X-axis and from the Y-axis are |y| and |x|, respectively; . The center of the coordinate system (where the lines intersect) is called the origin . The axes intersect when both x and y are zero. The coordinates of the origin. What is the coordinate of the point on the x-axis which is nearest to the point (-4, - 3)?. Views · If a point lies on X and y axis, what is the name and coordinate.
Thus the origin has coordinates 0, 0and the points on the positive half-axes, one unit away from the origin, have coordinates 1, 0 and 0, 1. In mathematics, physics, and engineering, the first axis is usually defined or depicted as horizontal and oriented to the right, and the second axis is vertical and oriented upwards.
However, in some computer graphics contexts, the ordinate axis may be oriented downwards. The origin is often labeled O, and the two coordinates are often denoted by the letters X and Y, or x and y. The axes may then be referred to as the X-axis and Y-axis.
The choices of letters come from the original convention, which is to use the latter part of the alphabet to indicate unknown values. The first part of the alphabet was used to designate known values. A Euclidean plane with a chosen Cartesian coordinate system is called a Cartesian plane. In a Cartesian plane one can define canonical representatives of certain geometric figures, such as the unit circle with radius equal to the length unit, and center at the originthe unit square whose diagonal has endpoints at 0, 0 and 1, 1the unit hyperbolaand so on.
The two axes divide the plane into four right anglescalled quadrant.
The quadrants may be named or numbered in various ways, but the quadrant where all coordinates are positive is usually called the first quadrant. If the coordinates of a point are x, ythen its distances from the X-axis and from the Y-axis are y and xrespectively; where The tick marks on the axes are one length unit apart.
A Cartesian coordinate system for a three-dimensional space consists of an ordered triplet of lines the axes that go through a common point the originand are pair-wise perpendicular; a orientation for each axis; and a single unit of length for all three axes. As in the two-dimensional case, each axis becomes a number line.
For any point P of space, one considers a plane through P perpendicular to each coordinate axis, and interprets the point where that plane cuts the axis as a number.
Cartesian coordinate system
The Cartesian coordinates of P are those three numbers, in the chosen order. The reverse construction determines the point P given its three coordinates. Alternatively, each coordinate of a point P can be taken as the distance from P to the plane defined by the other two axes, with the sign determined by the orientation of the corresponding axis.
Each pair of axes defines a coordinate plane.Where Does a Line Cross the X or Y Axis
Now that you know how to find the x-coordinate of a point, you have to be able to find the y-coordinate. The y-coordinate of a point is the value that tells you how far from the origin the point is on the vertical, or y-axis.
Where the x and y axes meet -- Crossword clue | Crossword Nexus
To find the y-coordinate of a point on a graph: Draw a straight line from the point directly to the y-axis. The number where the line hits the axis is the value of the y-coordinate. Looking back at the graph with our points B and D, we now identify the y-coordinate for each.
The y-coordinate of point B is The y-coordinate of point D is Notation for Identifying Points Once you have the coordinates of a point you can use the ordered pair notation for labeling points. The notation is simple. Points are identified by stating their coordinates in the form of x, y.
Note that the x-coordinate always comes first. For example, in the figure we've been using, we have identified both the x and y coordinate for each of the points B and D.
Coordinates of point B areThe x-coordinate of point D is Coordinates of point D arePoints On The Axes If a point is lying on an axis, you do not need to draw lines to determine the coordinates of the point. In the figure below, point A lies on the y-axis and point C lies on the x-axis.
When a point lies on an axis, one of its coordinates must be zero. Point A--If you look at how far the point is from the origin along the x-axis, the answer is zero.
Therefore, the x-coordinate is zero. Any point that lies on the y-axis has an x-coordinate of zero. If you move along the y-axis to find the y-coordinate, the point is from the origin.
The coordinates of point A are 0, Point C--If you look at how far the point is from the origin along the y-axis, the answer is zero. Therefore, the y-coordinate is zero. Any point that lies on the x-axis has a y-coordinate of zero. If you move along the x-axis to find the x-coordinate, the point is from the origin. The coordinates of point C are0 Example Which point is on the y-axis? Which point is labeled 20, 60? Which point s have a y-coordinate of 30? Answers to Example Which point is on the y-axis?
Point A Which point is labeled 20, 60? Point B Which point s have a y-coordinate of 30? This process is often referred to as plotting a point and uses the same skills as identifying the coordinates of a point on a graph. The process for plotting a point is shown using an example.