Divide line segment

Find the point P on line segment AB, such that |AP| = r |AB|. Coordinates of endpoints: A = (−2, 0, 1), B = (10, 8, 5), ratio r = 1/4.

Correct answer:

x =  7
y =  6
z =  4

Step-by-step explanation:

A=(2,0,1) B=(10,8,5) r=1/4=41=0.25  x=r Ax+(1r) Bx=0.25 (2)+(10.25) 10=7
y=r Ay+(1r) By=0.25 0+(10.25) 8=6
z=r Az+(1r) Bz=0.25 1+(10.25) 5=4   Verifying Solution:  d1=dist(A,B)=AB=(AxBx)2+(AyBy)2=((2)10)2+(08)2=4 1414.9666 d2=dist(A,P)=AP=(AxPx)2+(AyPy)2=((2)Px)2+(0Py)2=52.2361  D2=d1 r=14.9666 0.25=143.7417 d2=D2

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