Final answer:
Calculating slopes for both CD and EF and setting them equal to find x, results in x = -6, which does not match any of the given options and indicates an error in the question or options.
Step-by-step explanation:
To determine the value of x so that line segment CD is parallel to line segment EF, we need to ensure that the slopes of CD and EF are equal. The slope of a line through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). The slope of EF, using points E(-6, 14) and F(-2, 4), is (4 - 14) / (-2 - (-6)) = -10 / 4 = -2.5.
Next, we'll find the slope of CD using points C(x, 16) and D(2, -4). The slope formula for CD is (-4 - 16) / (2 - x) = -20 / (2 - x). To make CD parallel to EF, we set the slope of CD equal to the slope of EF, thus -20 / (2 - x) = -2.5.
Now, we solve for x: -20 / (2 - x) = -2.5 → -20 = -2.5 (2 - x) → -20 = -5 + 2.5x → 2.5x = -15 → x = -15 / 2.5 → x = -6. This value of x does not match any of the given options, implying an error in either the question or the options provided.