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.

Final 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:  P=(7,6,4) 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)7)2+(06)2=3 1411.225  D2=d1 r=14.9666 0.25=143.7417 d2=D2



Help us improve the example. If you find a mistake, let us know. Thank you!







Tips for related online calculators
Looking for help with calculating arithmetic mean?
The line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Looking for a statistical calculator?
Check out our ratio calculator.

You need to know the following knowledge to solve this word math problem:

statisticsgeometryarithmeticbasic operations and conceptsUnits of physical quantitiesGrade of the word problem

Related math problems and questions: