Simulation · Maths · Class 11
Turn the slope triangle through 90°
From the lesson Parallel and perpendicular lines in Straight Lines. Change the values and watch what happens.
Turn the slope triangle through 90°Maths · Class 11
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.