Given A(2,12) and B(5,0), find the coordinates of P such that P separates segment AB into two parts with lengths in a ratio of 2 to 1?

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Answer 1 · 2017-04-12T12:09:02

The target point is #(x,y)=(4,4)#

Assumption: the two parts is to the left side of the line

Let point 1 be #P_1->(x_1,y_1)=(2,12)#
Let point 2 be #P_2->(x_2,y_2)=(5,0)#
Let the target point be #P_t->(x_t,y_t)#

Combining the 2 parts and 1 part give a total of 3 parts. So as a fraction of the whole the 2 parts is #2/3#

So

#x_t" "=" "x_1+2/3(x_2-x_1)" " =" " 2+2/3(5-2)" " =" " 4#
#y_t" "=" "y_1+2/3(y_2-y_1)" "=" "12+2/3(0-12)" "=" "4#

Tony B
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Check:

#P_1->P_t = sqrt(2^2+8^2) #

#P_t->P_2=sqrt(4^2_1^2)#

So #(sqrt(2^2+8^2))/(sqrt(2^2+8^2)+ sqrt(4^2+1^2)) = 0.66bar6=2/3#