[Maths Class Notes] on Straight Lines Class 11 Pdf for Exam

In Euclidean geometry, a straight line is a set of all points between and stretching afar two points. In most geometry, a line is an elementary object that does not possess any formal properties beyond length, its single dimension. The two properties of straight lines in geometry are that they have only one length, dimension, and they stretch out only in two directions eternally. The idea of a straight line was first introduced by ancient mathematicians for the purpose of representing straight objects with negligible width and depth. 

Angles Formed By A Straight Line 

A straight line forms a 180-degree angle when constructing an angle arc from one point to another. Lines or straight lines are an idealization of such objects, which are frequently described in terms of two points or using a single letter.

Introduction To Point

A point is actually the simplest geometrical figure. It is a location in space, not having any dimension, depth, length, width, volume, or thickness. Even so, when you have two points, if you join every point in between those two points, you get a straight line.

Points on a line are referred to as collinear (col = “together” and linear = “line” or “string”). Only two points are required to identify a line.

How To Draw A Straight Line?

A straight line is one of the simplest drawings to construct in geometry. With a sheet of plain paper, a pencil, and a straightedge, you can draw a line or a straight line easily:

• Firstly, make 2 dots on the sheet, some distance from each other; these are points

• Then, the straightedge to join the 2 points with a pencil line, and stretch out the line beyond both points

• Make arrowheads at the ends of the line you construct

Know About The Direction of Straight Lines

1. Horizontal Straight Lines: Straight lines can be in a horizontal direction, meaning that they are moving left and right of the viewing spot, endlessly.

2. Vertical Straight Lines: Straight lines can be in a vertical direction, meaning that they are rising above and drowning below the viewing spot, forever.

3. Diagonal Straight Lines: Straight lines can be in a diagonal direction, which is to say that they are any angle besides horizontal or vertical.

4. Parallel Line: Straight lines can be single or in pairs. Pairs of straight lines can run parallel to one another. Distance between two parallel lines is such that they never get closer and are always further apart. They are represented with the symbol ∥.

5. Intersecting Straight Lines: Pairs of straight lines bisect each other at any angle. When two straight lines bisect at perpendicular distance of 90°, they are perpendicular, represented with the symbol ⊥.

What are Curves in Geometry?

A curve is an opposite of a straight line just as a straight line is not a curve. A curved line consists of points that are non-linear to the two given points. The curve moves in other directions from the straight line formed by connecting collinear points.

Solved Example On Straight Line 

Example:

Evaluate the angle between the y-axis and the line connecting the points (3, –1) and (4, –2).

Solution:

The slope of the line connecting the points (3, –1) and (4, –2) is 

m= -2-(-1)/4-3 

= -2 + 1 = -1 

Now, the inclination (θ ) of the line connecting the points (3, –1) and (4, – 2) is allocated as:-

tan θ = –1

⇒ θ = (90° + 45°) = 135°

Therefore, the angle between the y-axis and the line connecting the points (3, –1) and (4, –2) is 135°.