Question

When the three medians of the triangle are drawn, they meet at a single point. What is the point of the centroid?
a(5,5)
b(1,7)
c(3,2)
(1 point) Responses (3,5) left parenthesis 3 comma 5 right parenthesis (3,143) left parenthesis 3 comma start Fraction 14 over 3 End Fraction right parenthesis (3,6) left parenthesis 3 comma 6 right parenthesis (103,133)

Answer 1

To find the centroid of a triangle given its vertices, you can use the formula for the centroid (G), which is given by:

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

Given the vertices of the triangle:
- A(5, 5)
- B(1, 7)
- C(3, 2)

Let's substitute these coordinates into the centroid formula:

Calculating the x-coordinate of the centroid:
\[
x = \frac{5 + 1 + 3}{3} = \frac{9}{3} = 3
\]

Calculating the y-coordinate of the centroid:
\[
y = \frac{5 + 7 + 2}{3} = \frac{14}{3}
\]

Thus, the coordinates of the centroid G are:
\[
G\left(3, \frac{14}{3}\right)
\]

Therefore, the correct answer is:
\[
\left(3, \frac{14}{3}\right)
\]