1. Distance & Mid-Point Formulae
Millburn Academy
Maths department
Higher
Distance & Mid-Point Formulae

2. Find the distance between the points A(2,1) and B(6,6).
Use Pythagoras Theorem B
a² = b² + c² •
a² = 4² + 5²
a² =
a² = 41
a = √41 •
a = 6.4 A

3. This rule is called the distance formula.
We can find the distance between 2 points on the x-y axes by using the distance formula.
B(x2 , y2)
We can find the distance AB using Pythagoras Theorem.
y2 – y1
x2 – x1
A(x1 , y1) so
• Form a right angled triangle.
This rule is called the distance formula.
• The base of the triangle is
the difference in their x
coordinates ie
x2 – x1
• The height of the triangle
is the difference in their y
coordinates ie
y2 – y1

4. Find the length of AB given the points A(2,-1) and B(4,6)
Example
Find the length of AB given the points A(2,-1) and B(4,6)
(x1, y1)
(x2, y2)

5. The midpoint is the average of the x and y coordinates of A and B.
Mid-Point Formula
If we are given the coordinates of the points A(x1,y1) and B(x2,y2) then we can find the coordinates of the midpoint of AB.
B(x2,y2)
Midpoint
A(x1,y1)
Midpoint =
The midpoint is the average of the x and y coordinates of A and B.

6. Find the midpoint of AB given the coordinates A(5,2) and B(-3,6).
Example
Find the midpoint of AB given the coordinates A(5,2) and B(-3,6).
Midpoint = = =
= ( 1 , 4 )