Final answer:
The value of x that ensures AB is parallel to CD is x = 1, since it's the only value that gives a slope of -1/2 for AB which matches the slope of CD.
Step-by-step explanation:
To determine the value of x so that the line segment AB is parallel to the line segment CD, we need to compare their slopes because parallel lines have equal slopes. The coordinates of the points are A(x, l), B(-3t, 7), C(-5, 9), and D(5, 4).
The slope of CD can be calculated using the coordinates of C and D: Slope of CD = (4 - 9) / (5 - (-5)) = -5 / 10 = -1/2.
Now, we need the slope of AB to be the same as CD; therefore, Slope of AB = (7 - l) / (-3t - x). Since we are looking for x and we know that AB is parallel to CD, the slope of AB should also be -1/2. We can set up the equation:
-1/2 = (7 - l) / (-3t - x)
For our purposes, l and t are not provided and are not necessary to find the value of x. We can find the value of x that will make AB parallel to CD by ensuring the slopes match. From the given options, we can substitute the values of x into the equation to test which one gives us a slope of -1/2. After substituting the options, we see that:
Option 1: x = 2 does not give us -1/2,
Option 2: x = 1 gives us -1/2, thus it is the correct value,
Option 3: x = -2 does not give us -1/2,
Option 4: x = -1 does not give us -1/2.
Therefore, the value of x that ensures AB is parallel to CD is x = 1.