Answers

2014-08-23T20:41:24+05:30
See image.......I have solved on paper.....................
Mistake resolved. Verified graphically, answer is 100% right
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2014-08-24T15:27:55+05:30

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We can do by three methods.

One: By writing the formula for distance between two points AP(x,y) and PB and equating their ration to 1:2.  Difficult calculations.

Two : By shifting the origin to A(-1,3).  Then A' in new coordinate system is (0,0). B' will be (6,6). P' will be (2,2) dividing A'B' by 1:2. So P will be (2-1,2+3) = (1,5).

three: By using scalation / scaling method.  Ratio to divide AB: 1:2 or 1/3 : 2/3
 
         P( x , y )  :    x = -1 * 2/3 + 5 * 1/3  = 3/3 = 1
                           y =  3 * 2/3 + 9 * 1/3 =  15/3 = 5
Answer is (1,5)

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Well. .....alright.......but I think u are a maths teacher/professor/expert. Even i don't really understand the method