Questions: the following points? 9. (-3,2),(1,-6),(4,9)

Solution Steps

To find the centroid of the given points, we need to calculate the average of the x-coordinates and the average of the y-coordinates of the points.

The given points are: \[ (-3, 2), (1, -6), (4, 9) \]

The x-coordinates are: \[ x_1 = -3, \quad x_2 = 1, \quad x_3 = 4 \] Calculating the average: \[ \text{avg}_x = \frac{x_1 + x_2 + x_3}{3} = \frac{-3 + 1 + 4}{3} = \frac{2}{3} \approx 0.6667 \]

The y-coordinates are: \[ y_1 = 2, \quad y_2 = -6, \quad y_3 = 9 \] Calculating the average: \[ \text{avg}_y = \frac{y_1 + y_2 + y_3}{3} = \frac{2 - 6 + 9}{3} = \frac{5}{3} \approx 1.6667 \]

Final Answer