Questions: The vertices of triangle ABD are shown. A(-6,2) B(2,7) D(4,0) What are the coordinates of the centroid of triangle ABD?

Transcript text: The vertices of $\triangle A B D$ are shown. $A(-6,2) \quad B(2,7) \quad D(4,0)$ What are the coordinates of the centroid of $\triangle A B D$ ?

Solution

To find the coordinates of the centroid of a triangle given its vertices, we use the formula for the centroid $(G)$, which is the average of the x-coordinates and the y-coordinates of the vertices. The formula is:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) \]

For $\triangle ABD$, the vertices are $A(-6, 2)$, $B(2, 7)$, and $D(4, 0)$.

Calculate the average of the x-coordinates: \[ \frac{-6 + 2 + 4}{3} = \frac{0}{3} = 0 \]
Calculate the average of the y-coordinates: \[ \frac{2 + 7 + 0}{3} = \frac{9}{3} = 3 \]

Therefore, the coordinates of the centroid $G$ are $(0, 3)$.

The answer is: The coordinates of the centroid of $\triangle ABD$ are $(0, 3)$.

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