NCERT Class 11 Mathematics Mathematics: Chapter 9 — STRAIGHT LINES
This chapter, "Straight Lines," from NCERT Class 11 Mathematics, delves into the study of coordinate geometry, building upon previous knowledge of algebraic and geometric concepts. It begins with a recall of fundamental formulae such as the distance between two points, the section formula for internal division, the midpoint formula, and the area of a triangle. The chapter emphasizes the importance of these concepts as the foundation for understanding straight lines. It introduces the idea of representing lines algebraically, highlighting the crucial role of the slope of a line in this representation. The text aims to provide students with a comprehensive understanding of straight lines and their properties within the coordinate system, essential for further mathematical studies in the CBSE curriculum.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 9 — STRAIGHT LINES |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 698 |
Learning outcomes
- Recall and apply the distance formula between two points.
- Understand and use the section formula for internal division.
- Apply the midpoint formula to find the middle point of a line segment.
- Calculate the area of a triangle given its vertices.
- Understand the concept of collinearity through the area of a triangle.
- Grasp the fundamental concept of the slope of a line.
Vocabulary
| Word | Meaning |
|---|---|
| Coordinate Geometry | A system of geometry where the position of points on a plane is described using ordered pairs of numbers (coordinates). |
| Analytical Geometry | The study of geometry using algebraic methods, particularly coordinate systems. |
| Distance Formula | A formula to calculate the distance between two points in a coordinate plane. |
| Section Formula | A formula to find the coordinates of a point that divides a line segment internally in a given ratio. |
| Mid-point Formula | A special case of the section formula to find the coordinates of the midpoint of a line segment. |
| Collinear | Points that lie on the same straight line. |
| Slope | A measure of the steepness of a line, defined as the ratio of the vertical change to the horizontal change between any two points on the line. |
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Practice questions
- Calculate the distance between the points (2, 3) and (5, 7). Answer: The distance is 5 units.
- Find the coordinates of the point which divides the line segment joining (1, 2) and (4, 5) in the ratio 1:2 internally. Answer: The coordinates are (2, 3).
- Find the midpoint of the line segment joining the points (–1, 4) and (3, 0). Answer: The midpoint is (1, 2).
- Calculate the area of the triangle with vertices (0, 0), (1, 2), and (3, 0). Answer: The area is 3 square units.
Practice MCQs
Q1. What is the distance between the points (x1, y1) and (x2, y2)?
Explanation: The distance formula is derived from the Pythagorean theorem and calculates the length of the hypotenuse of a right-angled triangle formed by the difference in x and y coordinates.
Q2. If the area of a triangle formed by three points is zero, what can be concluded about the points?
Explanation: An area of zero for a triangle indicates that the vertices do not form a triangle but lie on a single straight line, hence they are collinear.
Q3. The coordinates of the midpoint of the line segment joining (x1, y1) and (x2, y2) are:
Explanation: The midpoint formula is derived by averaging the x-coordinates and the y-coordinates of the two endpoints.
Q4. Which French philosopher and mathematician introduced the notion of the equation of a curve in analytical geometry?
Explanation: René Descartes, in his book 'La Géométrie' (1637), is credited with introducing the use of algebra to describe geometric shapes, thus founding analytical geometry.
Q5. The section formula is used to find the coordinates of a point that divides a line segment:
Explanation: The section formula can be adapted to find coordinates for both internal and external division of a line segment in a specified ratio.
Frequently asked questions
What is the main focus of Chapter 9, "Straight Lines," in NCERT Class 11 Mathematics?
The chapter focuses on representing lines algebraically, with the slope of a line being a most essential concept for this representation.
What fundamental coordinate geometry concepts are recalled in this chapter?
The chapter recalls the distance between two points, section formulae, midpoint formula, and the area of a triangle.
Who is credited with introducing analytical geometry?
René Descartes is credited with introducing analytical geometry, which combines algebra and geometry, in his book 'La Géométry' published in 1637.
What does it mean if the area of a triangle formed by three points is zero?
If the area of a triangle formed by three points is zero, it means the three points lie on the same straight line, i.e., they are collinear.
What is the significance of the slope of a line?
The slope of a line is a crucial concept for representing lines algebraically and understanding their steepness and direction in a coordinate plane.
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NCERT Class 11 Mathematics — Mathematics — Chapter 9 — STRAIGHT LINES. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.