4 The distance between two points

Referring again to the figure of HELM booklet  2, the distance between the points A ( x 1 , y 1 ) and B ( x 2 , y 2 ) is given using Pythagoras’ theorem by the following formula.

Key Point 10

Distance Between Two Points

The distance between points A ( x 1 , y 1 ) and B ( x 2 , y 2 ) is ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2

Task!

Find the distance between A ( − 7 , 11 ) and B ( 1 , 3 ) , using Key Point 10.

( 1 − ( − 7 ) ) 2 + ( 3 − 11 ) 2 = 64 + 64 = 128

Exercises
  1. Find the distance between the points ( 4 , 5 ) and ( − 17 , 1 ) .
  2. Find the distance between the points ( − 4 , − 5 ) and ( 1 , 7 ) .
  1. 457
  2. 13