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

Find the distance between the points A(2,1) and B(6,6). Use Pythagoras Theorem B a² = b² + c² • a² = 4² + 5² a² = 16 + 25 a² = 41 a = √41 • a = 6.4 A

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

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)            

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.

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 )