Final answer:
To find the coordinates of the point Q, equate the given equations xy - 3x + 2y - 7 = 0 and XY = 1. By substituting the expressions for X and Y into the equation XY = 1, the coordinates of point Q are (y - 3, x + 2).
Step-by-step explanation:
To find the coordinates of the point Q, we need to equate the given equations.
The original equation is xy - 3x + 2y - 7 = 0. By shifting the origin to point Q, the new equation becomes XY = 1.
Now, we can equate the variables in both equations.
So, we have X = y - 3 and Y = x + 2.
Substitute these expressions for X and Y into the equation XY = 1 to get (y - 3)(x + 2) = 1.
By simplifying this equation, we get xy - 3x + 2y - 7 = 0.
This confirms that the new equation XY = 1 is indeed the shifted form of the original equation.
Therefore, by equating the corresponding variables in the original and new equations, we find that the coordinates of point Q are (y - 3, x + 2).