in the figure at the right, c is the centroid of $ \triangle def $.
if $ gf = 42x - 48y $, what expression represents $ cf $?

which expression below represents $ cf $?
$ \bigcirc a. 63x - 72y $
$ \bigcirc b. 28x - 32y $
$ \bigcirc c. 14x - 16y $
$ \bigcirc d. 21x - 24y $

Question

in the figure at the right, c is the centroid of $ \triangle def $.
if $ gf = 42x - 48y $, what expression represents $ cf $?

which expression below represents $ cf $?
$ \bigcirc a. 63x - 72y $
$ \bigcirc b. 28x - 32y $
$ \bigcirc c. 14x - 16y $
$ \bigcirc d. 21x - 24y $

Accepted Answer

# Explanation:
## Step1: Recall centroid property
The centroid divides each median into a ratio of $2:1$. That is, $CF=\frac{2}{3}GF$.
## Step2: Substitute $GF = 42x-48y$ into the formula
$$
\begin{align*}
CF&=\frac{2}{3}(42x - 48y)\
&=\frac{2\times42x}{3}-\frac{2\times48y}{3}\
&=28x-32y
\end{align*}
$$

# Answer:
B. $28x - 32y$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall centroid property

Step2: Substitute \(GF = 42x-48y\) into the formula

Answer: