Final answer:
The coordinates of the center of the triangle with the given vertices are (16/3, 6/3). The coordinates of the center (2x, 2y) are (32/3, 12/3).
Step-by-step explanation:
To find the coordinates of the center (x, y) of the triangle with vertices A(10, 12), B(8, -6), and C(-2, 0), we can use the midpoint formula. The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the two endpoints. Applying this formula to the given vertices, we have:
- x-coordinate of the center = (10 + 8 + (-2))/3 = 16/3
- y-coordinate of the center = (12 + (-6) + 0)/3 = 6/3
To find the coordinates of the center (2x, 2y), we can simply multiply the x-coordinate and y-coordinate of the center by 2:
- x-coordinate of the center (2x) = 2 * 16/3 = 32/3
- y-coordinate of the center (2y) = 2 * 6/3 = 12/3
Therefore, the coordinates of the center (x, y) of the triangle are (16/3, 6/3), and the coordinates of the center (2x, 2y) are (32/3, 12/3).