Question

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

Answer 1

Here is your solution

$AB = \sqrt{( 4 - 1) {}^{2} + (8 - 4) {}^{2} } \\ AB = \sqrt{9 + 16} \\ AB = \sqrt{25} \\ AB = 5$
Given:-
 AP=AB+BP,andAP=10

⇒10=5+BP

⇒BP=5

Since AP=AB+BP, 

⇒A,B and P are collinear, 
and since AB=BP,
⇒B is the mid point of AP

Let,
coordinates of P=(x,y)
$( \frac{x + 1}{2} ,\frac{y + 4}{2} ) = (4,8) \\ (x,y) = (7,12)$

Hope it helps you