Q. 3 D4.0( 4 Votes )

# 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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