Final answer:
To find the coordinates of the other centroid, solve the system of equations x + y = 5 and x² + y = 11 by substitution. So the coordinates of the other centroid are (3, 2) and (-2, 7).
Step-by-step explanation:
To find the coordinates of the other centroid, we need to solve the system of equations:
x + y = 5
x² + y = 11
One way to solve this system is by substitution. Rearrange the first equation to solve for x:
x = 5 - y
Substitute this expression for x in the second equation:
(5 - y)² + y = 11
Expand and simplify:
y² - 10y + 14 = 0
Factor the quadratic:
(y - 2)(y - 7) = 0
Solve for y:
y = 2 or y = 7
Substitute these values of y back into the first equation to find the corresponding values of x:
When y = 2, x = 5 - 2 = 3
When y = 7, x = 5 - 7 = -2
So the coordinates of the other centroid are (3, 2) and (-2, 7).