The problem asks to determine if the given lines, represented by sets of points, are parallel to each other or not. To check whether the lines are parallel, we need to compare their slopes. If the slopes of two lines are equal, then the lines are parallel.

The formula to find the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let's go through the points in each case:

1. a. Points: A(3,3), B(5,7), C(0,0), D(2,4)

   • Slope of AB = $\frac{7 - 3}{5 - 3} = \frac{4}{2} = 2$
   • Slope of CD = $\frac{4 - 0}{2 - 0} = \frac{4}{2} = 2$
     Since the slopes are equal, lines AB and CD are parallel.

2. b. Points: A(0,0), B(1,3), C(1,2), D(4,6)

   • Slope of AB = $\frac{3 - 0}{1 - 0} = \frac{3}{1} = 3$
   • Slope of CD = $\frac{6 - 2}{4 - 1} = \frac{4}{3}$
     Since the slopes are different, lines AB and CD are not parallel.

3. c. Points: A(-1,2), B(4,8), C(2,3), D(14,13)

   • Slope of AB = $\frac{8 - 2}{4 + 1} = \frac{6}{5}$
   • Slope of CD = ( \frac{