Question

find the centroid from a (5,5), b (1,7), and c (3,2) in this formula: x1+x2+x3/3, y1+y2+y3/3)

answers:
(3, 14/3)
(3, 5)
(3, 6)
(10/3, 14/3)

Answer 1

To find the centroid of the points A(5, 5), B(1, 7), and C(3, 2), we use the formula for the centroid of a triangle, which is given by:

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

Here, we have:
- \(A(5, 5)\) ⇒ \(x_1 = 5, y_1 = 5\)
- \(B(1, 7)\) ⇒ \(x_2 = 1, y_2 = 7\)
- \(C(3, 2)\) ⇒ \(x_3 = 3, y_3 = 2\)

Now we can compute the x-coordinate of the centroid:

\[
x = \frac{x_1 + x_2 + x_3}{3} = \frac{5 + 1 + 3}{3} = \frac{9}{3} = 3
\]

Next, we compute the y-coordinate of the centroid:

\[
y = \frac{y_1 + y_2 + y_3}{3} = \frac{5 + 7 + 2}{3} = \frac{14}{3}
\]

Combining these results, the centroid is located at:

\[
\left( 3, \frac{14}{3} \right)
\]

Thus, the correct answer is:

\((3, \frac{14}{3})\)