6.1 Distance between Two Points

6.1 Distance between Two Points

A(x1, y1) and C(x2, y2) are two points on a coordinate plane as shown below. BC is parallel to the x-axis and AB is parallel to the y-axis.  Hence  ∆ABC = 90°.


Distance between Point A and C =  

Example:
Find the distance between the points P (2, 2) and Q (–4, –5).

Solution:
Let P (2, 2) = (x1, y1 ) and Q (–4, –5) = (x2, y2 ).

Distance of PQ = ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 = ( 42 ) 2 + ( 5( 2 ) ) 2 = 36+9 = 45 = 9×5 =3 5  or ( 6.71 )