Final answer:
To find the value of k, we need to find the slopes of the lines AB and CD and set them equal since AB is parallel to CD. By calculating the slopes, we find that k = -1.
Step-by-step explanation:
To determine the value of k, we need to find the equation of the lines AB and CD and then check if they have the same slope. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: m = (y2 - y1) / (x2 - x1). So, the slope of AB = (3 - 3) / (-4 - 2) = 0, and the slope of CD = (k - (-1)) / (1 - 5) = (k + 1) / (-4).
To be parallel, the slopes of AB and CD must be equal. Therefore, 0 = (k + 1) / (-4). Solving this equation for k, we get k = -1.