Perpendicular Lines

What are perpendicular lines?

• You should already know that PARALLEL lines have equal gradients
• PERPENDICULAR LINES do meet each other and where they do the two lines form a right angle - ie they meet at 90°

What's the deal with perpendicular gradients (and lines)?

• Before you start trying to work with perpendicular gradients and lines, make sure you understand how to find the equation of a straight line - that will help you do the sorts of questions you will meet
• Gradients m₁ and m₂ are PERPENDICULAR if m₁ × m₂ = -1
• We can use m₂ = -1 ÷ m₁ to find a perpendicular gradient
• Another way to describe this is to say that the gradients of perpendicular lines are negative reciprocals
• For example;
  • 1 and - 1
  • 1/3 and - 3
  • 

Example: The line L has equation y = 2x - 2.
Find an equation of the line perpendicular to L which passes through the point (2,- 3).
Leave your answer in the form ax + by + c = 0 where a, b and c are integers.

Sketch is not essential but if it helps or you are stuck then draw one  

L is in the form y = mx + c so we can see that its gradient is 2
m₁ = 2
1, 2 - The gradient of the line perpendicular to L will be the negative reciprocal of 2
m₂ = -1÷2

See Finding Equations of Straight Lines
W e know the gradient of the line we're after but we still need to find c Find c by substituting the point (2,- 3) in :

c = -2

This is the line we want but it is not in the correct form Multiply by 2 to get rid of fractions (GROF) and rearrange until we do have it in the required format

2y = -x - 4
x + 2y + 4 = 0