Question

HELP PLEASE!!
Point Z is the centroid of triangle ABC and CZ = 18
what is the length of segment ZF? http://www.castlelearning.com/review/Courses/geometry/q4308.gif?v=20090302095508

Answer 1

can anyone help me with this?

Answer 2

ok so cz is 2/3rds of cf and zf is one third (note- in these cases the longer one is always 2/3rds and the shorter one is always 1/3d. so you take 1/3 of 18 and what is that?

Answer 3

so the answer is 6?

Answer 4

yep because in the whole CF there are thirds. and in these questions the longer one is always 2/3rds and the shorter is always 1/3rd. keep that in mind.

Answer 5

http://www.sparknotes.com/math/geometry2/theorems/section2.rhtml#median
>The centroid is 2/3 of the way from a given vertex to the opposite midpoint.

Therefore we know CZ = 2/3 CF, and knowing that CF = CZ + ZF, we find CZ = 2/3 CZ + 2/3 ZF and therefore 1/3 CZ = 2/3 ZF. Solving for ZF we determine ZF = 1/2 CZ. Given CZ = 18, we know ZF = 9.

Answer 6

Think about it... if CZ is 2/3 of CF, and CZ = 18, clearly CF = 27. Since CF = CZ + ZF, we can plug-in what we know to find 27 = 18 + ZF. Solve to get ZF = 9.

Answer 7

wow ive been doing it wrong lol. since day 1 of notes