Use the image to answer the question.

Question

A coordinate plane's axes range from 0 to 7, both by 1-unit increments. A triangle made up of vertices upper A, upper B, and upper C is plotted, and the coordinates of the points are given.

When the three medians of the triangle are drawn, they meet at a single point. What is the point of the centroid?

(1 point)
Responses

(3,6)
left parenthesis 3 comma 6 right parenthesis

(3,5)
left parenthesis 3 comma 5 right parenthesis

(3,143)
left parenthesis 3 comma start Fraction 14 over 3 End Fraction right parenthesis

(103,133)
left parenthesis Start Fraction 10 over 3 End Fraction comma Start Fraction 13 over 3 End Fraction right parenthesis

Answer 1

To find the centroid of a triangle with vertices A, B, and C, we use the formula for the centroid (G) which is given by the coordinates:

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

where \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) are the coordinates of the vertices of the triangle.

Since the specific coordinates of points A, B, and C are not provided, we can't directly compute the centroid. Assuming you have the coordinates, simply apply the formula above.

However, based on the provided responses, let's analyze them:

1. \((3, 6)\)
2. \((3, 5)\)
3. \(\left(3, \frac{14}{3}\right)\)
4. \(\left(\frac{10}{3}, \frac{13}{3}\right)\)

To confirm which of these points could likely be the centroid, we would typically calculate the centroid based on the coordinates of vertices A, B, and C.

Without the actual coordinates, I can't determine which option is correct, but you can find it accordingly once you input the coordinates into the centroid formula. If you have the coordinates of A, B, and C, please provide them, and I can help you calculate the centroid.