Lesson 4 of 10 · 7 min
Parallel and perpendicular lines
NCERT §9.2.2
Riya wants a straight lane from the well to the canal, meeting the canal at a right angle, and a road that never meets the canal at all. What must be true of their slopes?
The lesson in notes
In short
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.