Straight Lines

Maths · Class 11

Simulation · Maths · Class 11

The angle between two lines

"The angle between two lines" is a free, interactive Class 11 Maths simulation for JEE, built on the NCERT section "Angle between two lines" in Straight Lines. Two lines through a common point with slopes m₁ and m₂; the acute and obtuse angles are shaded and tan θ = |(m₂ − m₁)/(1 + m₁m₂)| is shown; a target-angle mode shows both lines that make the angle. JEE Main asked 42 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).

From the lesson Angle between two lines in Straight Lines. Change the values and watch what happens.

The angle between two linesMaths · Class 11

What it shows

NCERT §9.2.3

Two lines through a common point with slopes m₁ and m₂; the acute and obtuse angles are shaded and tan θ = |(m₂ − m₁)/(1 + m₁m₂)| is shown; a target-angle mode shows both lines that make the angle.

Controls

4 to try

  • Sliderm₁ −5 to 5
  • Sliderm₂ −5 to 5
  • Slidertarget angle 0°–90°
  • Toggleshow both solutions

Try this

With m₁ = 1/2, find both slopes m₂ that make 45° with it (3 and −1/3).

Common mistake

Keeping only one answer when a line makes a given angle with another.

In JEE Main

42 shifts analysed

42 questions from Straight Lines across the 42 JEE Main shifts Lumi has analysed (2017–2026).

See the past questions

The idea behind it

NCERT §9.2.3

  • Two intersecting lines make two pairs of vertically opposite angles, and adjacent angles add to 180°. If the lines have slopes m₁ and m₂, the angle θ = α₂ − α₁ between them has tan θ = (m₂ − m₁)/(1 + m₁m₂).
  • Taking the modulus gives the acute angle: tan θ = |(m₂ − m₁)/(1 + m₁m₂)|, provided 1 + m₁m₂ ≠ 0. The obtuse angle is 180° − θ.
  • If 1 + m₁m₂ = 0, the lines are perpendicular and θ = 90°.
  • Example: lines of slopes 1 and 0 make tan θ = 1, an angle of 45°. Lines of slopes 2 and 3 make tan θ = 1/7.
  • If the angle between two lines is π/4 and one slope is 1/2, then |(m − 1/2)/(1 + m/2)| = 1, which gives m = 3 or m = −1/3. There are two answers because the second line can be turned either way from the first.

Questions

4 answers

What does the "The angle between two lines" simulation show?
Two lines through a common point with slopes m₁ and m₂; the acute and obtuse angles are shaded and tan θ = |(m₂ − m₁)/(1 + m₁m₂)| is shown; a target-angle mode shows both lines that make the angle.
What mistake does the "The angle between two lines" simulation fix?
A common mistake it clears up: keeping only one answer when a line makes a given angle with another.
Does JEE Main ask questions from Straight Lines?
Yes. JEE Main asked 42 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
Is this simulation free?
Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Angle between two lines" in Straight Lines (Class 11 Maths).

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