6.2 Division of a Line Segment
(A) Midpoints 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(m−4, 3)=(−1+52, n+82)(m−4, 3)=(2, n+82)m−4=2 andn+82=3m=6and 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)+3p3+2, 2(2)+3q3+2)=(2,−1)(−2+3p5, 4+3q5)=(2,−1)Equating the x-coordinates,−2+3p5=2−2+3p=103p=12p=4Equating the y-coordinates,4+3q5=−14+3q=−53q=−9q=−3∴