Parallel lines share a gradient; perpendicular gradients multiply to −1. Use both to find equations, including perpendicular bisectors.
What you will learn
- Recognise parallel and perpendicular lines from their equations
- Find the equation of a parallel or perpendicular line through a point
- Find the perpendicular bisector of a line segment
Same gradient, or the negative reciprocal
Parallel lines have the same gradient: y = 3x + 1 and y = 3x − 4 never meet.
Perpendicular lines meet at a right angle, and their gradients multiply to −1. To find the perpendicular gradient, flip the fraction and change the sign: the negative reciprocal.
- gradient 3 = 3/1: perpendicular −1/3
- gradient −2/5: perpendicular 5/2
- check: −2/5 × 5/2 = −1
y = 2x and y = −x/2 + 1: 2 × (−1/2) = −1, so they cross at a right angle.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Same gradient, or the negative reciprocal
- A line through a point
- The perpendicular bisector
- Try it: Make a right angle
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Parallel, Perpendicular, Midpoint
In this unit: Straight-line graphs
Coordinates and midpoints, gradients and intercepts, the equation of a line, parallel and perpendicular lines, and straight-line graphs in real life.
- Coordinates, midpoints and plotting lines
- y = mx + c
- Finding the equation of a line
- Parallel and perpendicular lines
- Real-life graphs