Maths Class 11 Chapter 8 Questions and Answers - Free PDF Download
FAQs on NCERT Solutions For Class 11 Maths Chapter 8 Straight Lines Exercise 8.1 - 2025-26
1. How do you find the slope of a line using different forms of equations as per NCERT Class 11 Maths Chapter 8?
According to the NCERT solutions for the 2025-26 syllabus, the method to find the slope (m) depends on the information given:
- Slope-Intercept Form (y = mx + c): The slope is the coefficient 'm' of x.
- Point-Slope Form (y - y₁) = m(x - x₁): The slope is directly given as 'm'.
- Two-Point Form: If two points (x₁, y₁) and (x₂, y₂) are known, the correct method is to calculate the slope using the formula m = (y₂ - y₁) / (x₂ - x₁).
- General Equation (Ax + By + C = 0): The slope is calculated as m = -A/B.
2. What is the correct method to prove that three given points are the vertices of a right-angled triangle using the concept of slopes from Chapter 8?
To solve this as per the NCERT methodology, you should not use the Pythagoras theorem. Instead, follow these steps:
- Let the vertices be A, B, and C. Calculate the slopes of the three lines formed by these points: slope of AB (m₁), slope of BC (m₂), and slope of AC (m₃).
- Check if the product of the slopes of any two lines is equal to -1.
- If m₁ × m₂ = -1, or m₂ × m₃ = -1, or m₁ × m₃ = -1, it proves that two lines are perpendicular.
- The presence of a perpendicular pair of lines confirms that the vertices form a right-angled triangle.
3. How do you solve problems on the collinearity of three points using the slope formula in NCERT Chapter 8?
The step-by-step NCERT solution to check if three points A, B, and C are collinear is based on the principle that collinear points lie on the same straight line and thus must have the same slope. The correct method is:
- Calculate the slope of the line segment AB.
- Calculate the slope of the line segment BC.
- If the slope of AB is equal to the slope of BC, the points A, B, and C are collinear. This is a fundamental technique used in many problems in the chapter.
4. What is the approach for solving questions in the Miscellaneous Exercise of Chapter 8, Straight Lines?
The Miscellaneous Exercise in Chapter 8 requires a comprehensive understanding of all concepts. To solve these problems correctly:
- First, ensure you have mastered the individual concepts like slope calculation, different forms of line equations (point-slope, slope-intercept, intercept form), angle between two lines, and distance formulas.
- These problems often combine two or more concepts. For example, a question might require you to find the equation of a line and then calculate its distance from a point.
- The NCERT Solutions demonstrate how to break down these complex problems into smaller, manageable steps, which is key to finding the correct answer.
5. What is a common mistake made when finding the angle between two lines, and how do NCERT Solutions help prevent it?
A common mistake is forgetting to use the absolute value in the formula for the angle (θ) between two lines. Students often calculate tan θ = (m₂ - m₁)/(1 + m₁m₂), which may result in a negative value and only give the obtuse angle. The NCERT Solutions for the 2025-26 session consistently use the correct formula tan θ = |(m₂ - m₁)/(1 + m₁m₂)|. This ensures you always find the acute angle between the lines, which is the standard convention unless specified otherwise.
6. Why is the concept of slope (m = tan θ) so fundamental to solving most problems in Chapter 8, Straight Lines?
The concept of slope is fundamental because it numerically defines a line's two most critical properties: its steepness and direction. This single value 'm' is the key to:
- Determining the relationship between lines (parallel if m₁=m₂, perpendicular if m₁m₂=-1).
- Calculating the angle of inclination with the x-axis.
- Deriving the various forms of a line's equation, as almost every form (like point-slope and slope-intercept) directly uses the slope.
- Solving problems related to collinearity and geometric shapes.
7. When solving NCERT problems, how do you decide which form of a linear equation is the most efficient to use?
Choosing the right form saves time and prevents errors. The NCERT Solutions implicitly guide this choice:
- Use Point-Slope Form [ (y - y₁) = m(x - x₁) ] when you know one point on the line and its slope.
- Use Slope-Intercept Form [ y = mx + c ] when the slope and the y-intercept are known.
- Use Two-Point Form [ y - y₁ = (y₂-y₁)/(x₂-x₁) * (x - x₁) ] when the coordinates of two points on the line are given.
- Use Intercept Form [ x/a + y/b = 1 ] when the x-intercept (a) and y-intercept (b) are known. This is the most direct method for such problems.
8. How does the solution for finding the distance of a point from a line build upon concepts from earlier exercises in Chapter 8?
The formula for the distance of a point from a line is an application that synthesizes earlier concepts. The solution process demonstrates this connection:
- To use the distance formula, you first need the equation of the line in the general form (Ax + By + C = 0).
- Deriving this equation often requires using foundational skills from the chapter, such as calculating the slope (m) from given points or conditions.
- Therefore, finding the distance is not an isolated skill; it's a multi-step problem that relies on your ability to first define the line using the basic principles of slope and linear equations taught at the start of the chapter.











