medians of a triangle quick check
triangle abc is drawn on a coordinate plane with vertices ( a(-2,-3) ), ( b(4,1) ), and ( c(-2,2) ) and medians indicating the midpoint of each of the line segments ( overline{ab} ), ( overline{bc} ), and ( overline{ca} ). prove that the medians meet at a single point by finding the centroid (1 point)
( (-1,\frac{1}{3}) )
( (0,1) )
( (0,-\frac{1}{3}) )
( (0,0) )

Question

Accepted Answer

# Answer:
A. $(-1,\frac{2}{3})$

# Explanation:
## Step1: Recall the centroid formula
The centroid formula for a triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$ is $(\frac{x_1 + x_2+x_3}{3},\frac{y_1 + y_2 + y_3}{3})$
## Step2: Identify the coordinates of vertices
Given $A(-2,-3)$, $B(4,1)$, $C(-2,2)$, so $x_1=-2$, $y_1=-3$, $x_2 = 4$, $y_2=1$, $x_3=-2$, $y_3 = 2$
## Step3: Calculate the $x$ - coordinate of centroid
$$
\begin{align*}
x&=\frac{-2 + 4-2}{3}\
&=\frac{0}{3}\
&=- 1
\end{align*}
$$
## Step4: Calculate the $y$ - coordinate of centroid
$$
\begin{align*}
y&=\frac{-3+1 + 2}{3}\
&=\frac{0}{3}\
&=\frac{2}{3}
\end{align*}
$$

So the centroid is $(-1,\frac{2}{3})$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the centroid formula

Step2: Identify the coordinates of vertices

Step3: Calculate the \(x\) - coordinate of centroid

Step4: Calculate the \(y\) - coordinate of centroid

Answer: