6.2 Division of a Line Segment

6.2 Division of a Line Segment

(A) Midpoints of a Line Segment


Formula for the midpoint, M of A(xl, y1) and B(x2, y2) is


Example 1:
Given B (m – 4, 3) is the midpoint of the straight line joining A (–1, n) and C (5, 8). Find the values of m and n.

Solution:
B is the midpoint of AC ( m4, 3 )=( 1+5 2 ,  n+8 2 ) ( m4, 3 )=( 2,  n+8 2 ) m4=2         and         n+8 2 =3 m=6                and          n+8=6                                               n=2


(B) Point that Internally Divides a Line Segment in the 
Ratio m : n

Formula for the point P that lies on AB such that AP : PB = m : n is


Example 2:
The coordinate of R (2, –1) divide internally the line of AB with the ratio 3 : 2. If coordinate of A is (–1, 2), find the coordinate of B.

Solution:


Let point B=( p, q ) ( 2( 1 )+3p 3+2 ,  2( 2 )+3q 3+2 )=( 2,1 ) ( 2+3p 5 ,  4+3q 5 )=( 2,1 ) Equating the x-coordinates, 2+3p 5 =2 2+3p=10 3p=12 p=4 Equating the y-coordinates, 4+3q 5 =1 4+3q=5 3q=9 q=3  The coordinates of point B=(4,3).