60 POINTS AND WILL MARK BRAINLIEST Given the points A(-1,2) and B(7,14), find the coordinates of the Point P on the directed line segment AB that partitions AB in the ratio 1:3. In the above problem, what is the value of a/(a+b)?

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The line APB is a line such that AP/PB= 1/3. From the points A and B that we have we can find the distance between those points using the formula d= [(y2-y1)^2=(x2-x1)^2]^1/2

d= 4 (13)^(1/2)

Now the ratio is 1:3. AP= sq rt(13) and PB= 3 sq rt(13)

Using mid point formula the mid point of AB (say Q) = [(-1+7)/2,(2+14)/2]= (3,8).  

Hence the mid point of AQ is P which can found out again using the mid point formula  

P= [(-1+3)/2,(2+8)/2]= (1,5)

Final P=(1,5)

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