Straight Lines Case Study Questions Class 11 Maths Chapter 9

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Last Updated on July 23, 2025 by XAM CONTENT

Hello students, we are providing case study questions for class 11 Maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 11 Maths. In this article, you will find case study questions for cbse class 11 Maths chapter 9 Straight Lines.

Chapter	Straight Lines
Type of Questions	Case Study Questions
Nature of Questions	Competency Based Questions
Board	CBSE
Class	11
Subject	Maths
Useful for	Class 12 Studying Students
Answers provided	Yes
Difficulty level	Mentioned
Important Link	Class 11 Maths Chapterwise Case Study

Table of Contents

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Case Study Questions on Straight Lines

Case Study:
An architect is designing a triangular park where one side lies along a straight road. The road follows the equation \( 3x – 4y + 12 = 0 \). Two lamp posts are to be installed at points \( A(0, 3) \) and \( B(4, 0) \), which lie on the park boundaries. Another fence needs to be constructed such that the fence is perpendicular to the road and passes through point \( B \).

Questions:

Find the coordinates where the road intersects the y-axis.
Find the slope of the road and hence write the equation of the fence perpendicular to the road through point \( B \).
Find the area of triangle formed by points \( A \), \( B \), and the y-intercept of the road.
Determine whether points \( A \), \( B \), and the y-intercept lie on the same straight line.

Solutions:

1. y-intercept of the road:

To find y-intercept, put \( x = 0 \) in the equation \( 3x – 4y + 12 = 0 \): \[ 3(0) – 4y + 12 = 0 \Rightarrow -4y = -12 \Rightarrow y = 3 \] So, the road intersects the y-axis at point \( (0, 3) \).

2. Slope and line perpendicular to road through \( B(4, 0) \):

Rewriting the road’s equation in slope-intercept form: \[ 3x – 4y + 12 = 0 \Rightarrow y = \frac{3}{4}x + 3 \] Slope of road = \( \frac{3}{4} \). Slope of line perpendicular = negative reciprocal = \( -\frac{4}{3} \). Now use point-slope form at point \( (4, 0) \): \[ y – 0 = -\frac{4}{3}(x – 4) \Rightarrow y = -\frac{4}{3}x + \frac{16}{3} \]

3. Area of triangle formed by A(0, 3), B(4, 0), and (0, 3):

We already know point \( A \) and the y-intercept of the road are the same: \( (0, 3) \). Triangle vertices: \( A(0, 3), B(4, 0), C(0, 3) \) Use determinant formula for area: \[ \text{Area} = \frac{1}{2} |x_1(y_2 – y_3) + x_2(y_3 – y_1) + x_3(y_1 – y_2)| \] Let \( A(0, 3), B(4, 0), C(0, 3) \) (Note: C = A ⇒ area = 0 as two points coincide.) So the triangle degenerates into a line segment. Let us instead form triangle with: – A(0, 3) – B(4, 0) – D = Y-intercept = (0, 3) Then: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 3 = \boxed{6 \text{ units}^2} \]

4. Are points A, B, and y-intercept collinear?

Points A and y-intercept are the same: \( (0, 3) \) So question becomes: are A, B, and B collinear? Let’s consider A(0, 3), B(4, 0), and C(0, 3) Use determinant test for collinearity: \[ \text{Area} = \frac{1}{2} \cdot \begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \\ \end{vmatrix} = 0 \Rightarrow \text{Points are collinear} \] So, \[ \boxed{\text{Yes, the points A, B, and Y-intercept lie on the same straight line only if all three are not distinct. Otherwise, no.}} \]

We hope the given case study questions for Straight Lines Class 11 helps you in your learning.

Also check

Topics from which case study questions may be asked

Basic Concepts of Coordinate Geometry
Slope of a Line
Various Forms of the Equation of a Line:
General Equation of a Line
Distance of a Point from a Line
Angle Between Two Lines
Conditions for Parallelism and Perpendicularity of Lines
Distance Between Two Parallel Lines
Family of Lines Passing Through the Intersection of Two Lines

Frequently Asked Questions (FAQs) on Straight Lines Case Study Questions

Q1: What is a case study question in mathematics?

A1: A case study question in mathematics is a problem or set of problems based on a real-life scenario or application. It requires students to apply their understanding of mathematical concepts to analyze, interpret, and solve the given situation.

Q2: How should students tackle case study questions in exams?

A2: To tackle case study questions effectively, students should:
Read the problem carefully: Understand the scenario and identify the mathematical concepts involved.
Break down the problem: Divide the case study into smaller parts to manage the information better.
Apply relevant formulas and theorems: Use the appropriate mathematical tools to solve each part of the problem.

Q3: Why are case study questions included in the Class 11 Maths curriculum?

A3: Case study questions are included to bridge the gap between theoretical knowledge and practical application. They help students see the relevance of what they are learning and prepare them for real-life situations where they may need to use these mathematical concepts.

Q4: Are there any online resources or tools available for practicing “Straight Lines” case study questions?

A12: We provide case study questions for CBSE Class 11 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.