Turn the slope triangle through 90°
"Turn the slope triangle through 90°" is a free, interactive Class 11 Maths simulation for JEE, built on the NCERT section "Parallel and perpendicular lines" in Straight Lines. A slope triangle (run, rise) rotated by 90° becomes (−rise, run), turning slope m into −1/m; a horizontal/vertical pair shows why m₁m₂ = −1 cannot test it. JEE Main asked 42 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Parallel and perpendicular lines in Straight Lines. Change the values and watch what happens.
What it shows
NCERT §9.2.2
A slope triangle (run, rise) rotated by 90° becomes (−rise, run), turning slope m into −1/m; a horizontal/vertical pair shows why m₁m₂ = −1 cannot test it.
Controls
3 to try
- Sliderrise −5 to 5
- Sliderrun −5 to 5
- Buttonrotate 90°
Try this
Rotate the slope-2/3 triangle and read the perpendicular slope −3/2; then show the horizontal case where the product is undefined.
Common mistake
Using m₁m₂ = −1 for a horizontal and a vertical line.
In JEE Main
42 shifts analysed
42 questions from Straight Lines across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §9.2.2
- Lines that are not vertical are parallel exactly when they have the same slope, m₁ = m₂: the same slope means the same inclination.
- Two non-vertical lines are perpendicular if and only if m₁m₂ = −1, that is m₂ = −1/m₁. Turning a line through 90° changes tan α into tan(α + 90°) = −cot α.
- A line of slope 2/3 has perpendiculars of slope −3/2: flip the fraction and change its sign.
- Example: the line through (−2, 6) and (4, 8) has slope 2/6 = 1/3. The line through (8, 12) and (x, 24) has slope 12/(x − 8). For them to be perpendicular, (1/3) × 12/(x − 8) = −1, so x − 8 = −4 and x = 4.
- A horizontal line (slope 0) and a vertical line (no slope) are perpendicular too, but m₁m₂ = −1 cannot show it, since one slope is not defined.
Questions
4 answers
- What does the "Turn the slope triangle through 90°" simulation show?
- A slope triangle (run, rise) rotated by 90° becomes (−rise, run), turning slope m into −1/m; a horizontal/vertical pair shows why m₁m₂ = −1 cannot test it.
- What mistake does the "Turn the slope triangle through 90°" simulation fix?
- A common mistake it clears up: using m₁m₂ = −1 for a horizontal and a vertical line.
- 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 "Parallel and perpendicular lines" in Straight Lines (Class 11 Maths).
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