Let P and Q be the points of trisection of the line segment joining the points A (2, -2) and B (-7, 4) such that P is nearer to A. Find the coordinates of P and Q.
Answers
Given : P and Q be the points of trisection of the line segment joining the points A (2, -2) and B (-7, 4) such that P is nearer to A.
To Find : the coordinates of P and Q
Solution:
A (2, -2) and B (-7, 4)
P and Q be the points of trisection
AP = PQ = QB
AP + PQ + QB = AB
=> AP : PB = 1 : 2
PQ = QB => Q is the mid point of PB
AP : PB = 1 : 2 => P divides AB internally in 1 :2 ratio
A (2, -2) and B (-7, 4)
=> P = ( 1 * - 7 + 2 * 2)/3 . ( 1*4 + 2 * - 2)/3
=> P =( - 1, 0)
P =( - 1, 0) B (-7, 4)
Q = ( - 1 - 7)/2 , (0 + 4)/2
=> Q = - 4 , 2
P =( - 1, 0) Q = (-4,2)
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