Calculating the Length of a Line:
To calculate the length of the line joining two points, the application of Pythagoras' Theorem is used.
The Length of the line is seen to be c and so a formula for c was derived as follows:
The Length of the line is seen to be c and so a formula for c was derived as follows:
Worked Examples:
Find the length of the line joining points (2, 1) & (5, 5)
Length = √( (x2 - x1)² + (y2 - y1)² ) Length = √( (5-2)² + (5-1)² ) Length = √( 3² + 4² ) Length = √( 9 + 16 ) Length = √( 25 ) Length = 5 Find the length of the line joining points (0, -2) & (8, 13) Length = √( (x2 - x1)² + (y2 - y1)² ) Length = √( (8-0)² + (13- -2)² ) Length = √( 8² + 15² ) Length = √( 64 + 225 ) Length = √( 289 ) Length = 17 |
Find the length of the line joining points (-7, 3) & (-2, 5)
Length = √( (x2 - x1)² + (y2 - y1)² ) Length = √( (-2- -7)² + (5-3)² ) Length = √( 5² + 2² ) Length = √( 25 + 4 ) Length = √( 29 ) Length = √29 Find the length of the line joining points (-7, 4) & (-1, 1) Length = √( (x2 - x1)² + (y2 - y1)² ) Length = √( (-1- -7)² + (1-4)² ) Length = √( 6² + -3² ) Length = √( 36 + 9 ) Length = √( 45 ) Length = 3 √5 |