A plane meets the coordinate axes $A, B, C$ such that the centroid of the triangle $ABC$ is the point $(a, b, c)$ , show that the equation of the plane is $x/a+y/b+z/c=3$ ?

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Answer 1 · 2017-07-07T09:24:20

See the proof below

The equation of the plane is

$x/A+y/B+z/C=1$

By the definition of the centroid

$(A/3,B/3,C/3)=(a,b,c)$

Therefore,

$A=3a$

$B=3b$

$C=3c$

The equation of the plane becomes

$x/(3a)+y/(3b)+z/(3c)=1$

$1/3(x/a+y/b+z/c)=1$

So,

$x/a+y/b+z/c=3$

A plane meets the coordinate axes A, B, CA, B, C such that the centroid of the triangle ABCABC is the point (a, b, c)(a, b, c), show that the equation of the plane is x/a+y/b+z/c=3x/a+y/b+z/c=3?