Question

In the figure below c is the centroid of triangle def if GF=12x^2+6y which expression represents cf

Answer 1

option 3 ⇒ 8x² + 4y

Explanation:

As shown in the figure

C is the centroid of ΔDEF

We should know that the centroid divides each median in the ratio 2:1

So, CF = 2 CG ⇒ CG = 0.5 CF

But GF = CF + CG

∴ GF = CF + 0.5 CF = 1.5 CF = (3/2) CF

∴ CF = (2/3) GF

∵ GF = 12 x² + 6y

∴ CF = (2/3) * (12 x² + 6y) = 8x² + 4y

So, the correct answer is option 3