Question

The points A, B and C divides the line segment MN in four equal parts. The coordinates of Mand N are (-1, 10) and (7, -2) respectively. Find the coordinates of A, B and C. 

Answer 1

Given, A (x, y ), B (a, b) and C (p, q) divides the line segment MN ir four equal parts. B in the mid point of MN. i.e. MB :BN = 1: 1 Coordinates of B are, 

B (a , b) = B `((7 - 1)/2 , (-2 + 10)/2)` = B (3 , 4)

A is the mid point of MB i.e. MA : AB= 1 : 1

coordinates of  A are. 

A (x , y) = A `((3 - 1)/2 , (4 + 10)/2)` = A (1 ,7)

C is the mid point of BN i.e BC: CN= 1: 1 

C (p,q) = C `((3 + 7)/2 , (4 - 2)/2)` = C (5 , 1)

Hence, the coordinates of A, B and C are ( 1, 7), (3, 4) and (5, 1) respectively