Thinking perpendicular lines have the same gradient H
"The Perpendicular Puzzle"
The Mistake in Action
Line A has equation $y = 2x + 1$. Line B is perpendicular to Line A. Find the gradient of Line B.
Wrong: Gradient of Line B = $2$ (same as Line A)
Why It Happens
Students confuse perpendicular with parallel, or don't know the relationship between perpendicular gradients.
The Fix
Parallel lines have the same gradient. Perpendicular lines have gradients that multiply to give $-1$.
If Line A has gradient $m$, then a perpendicular line has gradient $-\frac{1}{m}$.
Line A: gradient = $2$ Line B: gradient = $-\frac{1}{2}$
Check: $2 \times (-\frac{1}{2}) = -1$ ✓
Memory aid: "Flip and negate" — turn the gradient upside down and change the sign.
Spot the Mistake
Can you identify where this student went wrong?
Line A: $y = 2x + 1$. Line B is perpendicular.
Gradient of Line B = 2
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: