ALL JEE 2026 January PYQs | Straight Lines | JEE Mains Questions Chapter Wise

Understanding Straight Line Questions

Introduction to Straight Line Problems

• The discussion focuses on solving straight line questions, which are often lengthy and complicated, making it challenging to determine the approach.

• The session aims to teach strategies for using geometry effectively in these problems, particularly through examples from JEE Mains 2026.

First Problem Overview

• The first question involves a point located between two parallel lines L1 and L2, with specified distances from each line.

• An equilateral triangle ABC is formed where point B lies on line L1 and point C on line L2; the area of this triangle needs to be calculated.

Geometry Setup

• Points are assigned: A is the midpoint between L1 and L2, with known distances (6 units from L1 and 3 units from L2).

• The angles of triangle ABC are established as 60° each due to its equilateral nature, leading to equal side lengths AB, BC, and AC.

Area Calculation Methodology

• To find the area of triangle ABC, one must derive the length of any side using geometric principles.

• By introducing an angle θ at point A and establishing relationships between sides using trigonometric identities like cos(θ), calculations can proceed.

Solving for Side Lengths

• Using right triangles formed by dropping perpendicular lines helps express side lengths in terms of θ.

• Equating expressions for sides AB and AC leads to a relationship that simplifies down to finding cos(θ).

Trigonometric Relationships

Deriving Cosine Values

• Establishing that cos(θ + 120°)=2cos allows for further simplification in determining θ's value.

• Utilizing cosine values such as cos(120°), which equals -1/2, aids in calculating necessary trigonometric ratios.

Final Area Computation

• After deriving tan values based on previous calculations, one can compute the area using standard formulas involving base and height.

Statement Type Scenarios

Evaluating Statements about Triangles

• The next problem presents two statements regarding points A and B forming a triangle with an orthocenter; verification is required if these points satisfy certain conditions.

Orthocenter Calculation Steps

• To find the orthocenter D of triangle ABC, perpendicular lines from vertices A and B need their equations derived based on slopes.

Rectangle Formation

Rectangle Defined by Lines

• Another question describes a rectangle formed by four given lines intersecting at specific coordinates.

Perpendicular Line Analysis

• A new line l is introduced that divides the rectangle into equal parts; its slope must be determined based on existing lines' slopes.

Rhombus Properties

Diagonal Points in Rhombus

• In another scenario involving a rhombus defined by diagonal points A and C along with parallel sides AD and BC.

Midpoint Calculations

• Finding midpoints helps establish relationships among vertices crucial for solving related queries about sums or coordinates.

This structured markdown file captures key insights while maintaining clarity through timestamps linked directly back to relevant sections of the transcript.

Understanding the Length of AD

Calculation of Length

• The length of segment AD is determined to be 4, derived from the equation 4/3 = AD/3 .

• By substituting values into the equation, we find that alpha + 8beta - 4 = 12 , leading to a simplified form of 9alpha - 4 = 12 .

Solving for Alpha and Beta

• Adding terms results in 9alpha = 16beta , which simplifies to give a value for beta as 32/9 .

• Conversely, subtracting yields 9alpha = -8 , resulting in an alpha value of -8/9 .

Analyzing Triangle Orientation

Positioning Points

• The triangle's orientation indicates that both points must lie on the same side relative to the origin; negative outputs suggest incorrect positioning.

• If alpha and beta are placed incorrectly, it could lead to contradictions regarding their positions.

Validating Values

• Substituting values back into equations confirms whether they yield positive or negative outputs; this helps validate if both points are correctly positioned.

Finalizing Alpha and Beta Values

Confirming Results

• After checking calculations with substituted values, we confirm that alpha equals -8/9 and beta equals -32/9 .

Conclusion on Integer Values

Greatest Integer Function Application

• Applying the greatest integer function leads us to conclude that the final answer is four when considering all calculated values.

Summary of Problem-Solving Approach

Review of Methodology

• The approach taken reflects effective problem-solving strategies used in JEE Main questions related to straight lines. Further resources can be explored for additional practice.

Additional Resources

Exploring More Chapters

• Viewers are encouraged to check out other chapters available in playlists for comprehensive learning on related topics.