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 coordinates of P ?

1 Answer
CW
Sep 4, 2017

#(7,12)#

Explanation:

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#AB=sqrt((4-1)^2+(8-4)^2)=sqrt(9+16)=sqrt25=5#
Given #AP=AB+BP, and AP=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)#
#=> ((x+1)/2,(y+4)/2)=(4,8)#
#=> (x,y)=(7,12)#

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