### Instruction: Find the coordinates of the center of the hyperbola \[\frac{(2y-2)^2}{5^2} - \frac{(3x-4)^2}{4^2} = 1.\].### Response: To find the center of a hyperbola, I need to look at the terms inside the parentheses and find the values of x and y that make them zero.
For the first term, I have 2y - 2, so I can add 2 to both sides and divide by 2 to get y = 1.
For the second term, I have 3x - 4, so I can add 4 to both sides and divide by 3 to get x = 4/3.