Two Dimensional Lines

This article will provide information on two-dimensional lines, its properties and significance. Lines are geometric shapes made of points and line segments. All lines are either straight or curved. A straight line has infinite length, while a curved line extends only over part of the plane. The simplest and most familiar type of linear curve is a circle, which is formed by a loop drawn in the plane so that it goes around one point or more times; other curves may pass over different points (of which there may be any number).

What are Lines?

Lines are made of points and line segments. A line is the shortest distance between two points.

Significance of Lines:

Lines represent the most fundamental concept in mathematics and geometry. They are used to describe a variety of different geometric figures:

Canonical Perspective:

In the painting and drawing of scenes, lines are used to define various objects from an overall viewpoint. The lines may be drawn parallel to one another, but never cross each other. These two types of straight lines , “mathematically equivalent” or transversal lines (lines that intersect) and vertical or horizontal lines are called canonical. They form the basis for perspective drawing, which is concerned with accurately depicting a three-dimensional scene as it appears from a fixed, idealized viewpoint.

Types of Lines:

There are different types of lines, for example:

1) Straight Line / Tangent Line – is a line that intersects or touches another but does not completely cross that line. 

2) Angle / Shortened Angle – a segment (piece) of a line which does not intersect another but has a certain relationship to another. Ideal angle / Parallel Lines – are parallel to each other, i.e., all points in one line lie directly on the same straight line and all points in the second lie on the same straight line, with no point in the first lying directly on any point in the second (i.e. they are not angles). 

3) Ray (Half Ray) – a straight line that originates from a point and continues indefinitely in one direction. 

4) Line Segment – which is the part of a ray between two specified points called ends.

Tips on Drawing Lines:

• There are several ways to draw lines: Use a ruler or compass to draw the line, use the draw tool, or you can also use the “line” function to create lines. 

• Another trick is to align the coordinate axes so that both of them form straight lines as shown above, and then copy and paste them as many times as needed.

• If you want to draw several lines, you can use the gridlines and copy and paste as many times needed when you align the gridlines.

What are 2D Lines?

A 2D Line has 2 dimensions, where one dimension is represented by an axis(x-axis) and the other dimension by another axis(y-axis) with both axes being perpendicular to each other. The 2d lines are a special kind of line that have coordinates on the x and y axis, where the coordinate is(x,y).

Linear equations:

Linear equations are used to represent sets of related points on a plane or in three-dimensional space. They consist of sets of numbers (1,2,3). We can use linear equations to create graphs and 2D lines.

Properties of 2D Lines:

1) A line can be represented by any of the following: 

• (x, y) where x is a value on the x-axis and y is a value on the y-axis.

The point (0,0) represents the origin. If y = 0 then the point is also at the origin. This means that every straight line has an equation of either: 

• x = m and  y = 0 or  x = 0 and  y = m (where m is any real number).

2) The slope of a line: We define each point in two dimensional space as having both an ” x ” coordinate and a ” y ” coordinate. The slope is a measure of how much the ” y ” coordinate changes as we change the ” x ” coordinate by one unit. The slope can be divided into components (that is, split into parts):

3) The slope of a line is  always positive  (or zero). It would be impossible for it to be negative because then the graph would not lie on the xy-plane.

4) If two lines have slopes that are different from each other, then they must intersect at some point. Any two distinct lines will have a unique point of intersection.

Dimensions of 2D Lines:

2D lines can be defined as having two dimensions (2 dimensions: length and width or x-axis and y-axis). The 2 dimensions of lines are based on the graph of the line, which is a set of points that plots a line in the xy-plane.

Conclusion:

Lines are created by using the coordinate or arrow functions, which can be used to draw various types of 2D lines. Lines can be drawn using the scatter plot graph and you can also use the line() function. You should know how to use them as they are very important in Graphs and Cartesian Coordinates.