Final answer:
After calculating the slopes, it is determined that for Line AB to be parallel to Line CD, the slope of AB must also be -0.5. Solving for x using the slope formula, we get x = 9, which is not one of the provided options. There could be an error in the question or the given choices.
Step-by-step explanation:
The student has asked to find the value of x so that Line AB is parallel to Line CD. To determine if two lines are parallel, we need to compare their slopes; parallel lines have the same slope.
First, calculate the slope of Line CD using the points C(-5, 9) and D(5, 4):
Slope of CD = (y2 - y1) / (x2 - x1) = (4 - 9) / (5 - (-5)) = (-5) / (10) = -0.5.
Now, we need to find the slope of Line AB using point A(x, 1) and point B(-3, 7):
Slope of AB = (7 - 1) / (-3 - x) = 6 / (-3 - x)
For Line AB to be parallel to Line CD, the slope of AB must also be -0.5. So, set the slope of AB equal to -0.5 and solve for x:
-0.5 = 6 / (-3 - x)
Multiplying both sides by (-3 - x) gives us:
-0.5(-3 - x) = 6
Now, we simplify:
1.5 + 0.5x = 6
Subtract 1.5 from both sides:
0.5x = 4.5
Finally, divide by 0.5 to solve for x:
x = 4.5 / 0.5 = 9.
However, the value x = 9 is not one of the given options. Therefore, it seems there might have been an error in the question or the provided options.