Q3 of 184 Page 10

A (1,4) and B (4,8) are two points. P is a point on AB such that AP = AB + BP. If AP = 10 find the coordinates of P.


Given: AP = AB + BP and AP = 10


Firstly, we find the distance between A and B


d(A,B) = √(x2 – x1)2 + (y2 – y1)2


= √(4 – 1)2 + (8 – 4)2


= √(3)2 + (4)2


= √9 + 16


= √25


= 5


So, AB = 5


It is given that AP = AB + BP


⇒ 10 = 5 + BP


⇒ 10 – 5 = BP


⇒ BP = 5


⇒ A, B and P are collinear


and since AB = BP


⇒ B is the midpoint of AP


Let the coordinates of P = (x,y)




⇒ x + 1 = 8 and y + 4 = 16


⇒ x = 7 and y = 12


Hence, the coordinates of P are (7, 12)


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