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)
