Step-by-step Solution:

If a point \( (x_0, y_0) \) is equidistant from the coordinate axes, then \( |x_0| = |y_0| \).\nThis gives two cases: \( y_0 = x_0 \) or \( y_0 = -x_0 \).\n\nCase 1: \( y_0 = x_0 \)\nSubstitute into the line equation: \( 8x_0 - 3x_0 = 11 \implies 5x_0 = 11 \implies x_0 = \frac{11}{5} \).\nSince \( (x_0, y_0) \in \mathbb{Z}^2 \), \( x_0 \) must be an integer, so this case is rejected.\n\nCase 2: \( y_0 = -x_0 \)\nSubstitute into the line equation: \( 8x_0 - 3(-x_0) = 11 \implies 11x_0 = 11 \implies x_0 = 1 \).\nThen \( y_0 = -1 \).\n\nThe point is \( (1, -1) \), which is an integer coordinate point.\nThis point lies in the IV quadrant (where \( x > 0 \) and \( y < 0 \)).