Straight Lines Class 11

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What is a Straight Line?

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°.

FAQ (Frequently Asked Questions)

Q1. What are the topics covered in CBSE class 11 Chapter-10 Straight Lines?

Answer: Following are the topics included in the chapter:

  • Slope of a Line

  • Distance between two lines and distance of a point from a line

  • General Equation of a Line and Different types of the equation of a line

  • First Degree Equation

Q2. Where can I find the revision notes for Class 11 Mathematics?

Answer: CBSE class 11th Chapter 10 Straight Lines revision notes are available for download in free PDF format. You can simply download revision notes for Straight Lines and score high in exams. The Straight Lines class 11 Notes Mathematics is prepared by a team of expert teachers at Vedantu. These chapter notes will help you revise the whole chapter just in minutes even at the last moment of the exam. Revising Vedantu's notes in exam days is one of the recommended tips to perform exceptionally well in the final exam.

Q3. What do we understand by Straight Angles?

Answer: Straight lines seem like another geometrical figure, and vice versa. A straight angle at an angle of 180° is a straight line. A straight angle is formed with two rays and a common endpoint. Seeing that the two rays share a common endpoint and each ray proceeds in one direction eternally, the only "gratuity" that you have a straight angle (and not a straight line) might be the 3 determined points (instead of two).

Q4. What do we understand by Concurrent Lines?

Answer: Three or more than three straight lines are said to be concurrent if they cross across a common point i.e., they unite at a point. Therefore, if three lines are concurrent, then the point of bisection of two lines lies on the third line.