Final answer:
Using the partition formula with a 1/4 ratio between points A(-2,1) and B(4,-3), the calculated x-coordinate of the partition point is -0.5, which does not match any of the provided multiple-choice options. There may be a mistake in the question or the process.
Step-by-step explanation:
The question involves using the partition formula to determine the point that divides a segment into a given ratio. Here, line AB is partitioned at a ratio of 1/4 with A(-2,1) and B(4,-3). To find the x value of the partition point, we employ the formula (x, y) = (x1 + k * (x2 - x1), y1 + k * (y2 - y1)), where k is the part-to-whole ratio, which is 1/4 in this case.
To find the x-coordinate of the partition point, we plug in the values and calculate:
- x1 = -2 (x-coordinate of A)
- x2 = 4 (x-coordinate of B)
- k = 1/4 (part-to-whole ratio)
Then the formula gives us:
x = -2 + (1/4) * (4 - (-2))
x = -2 + (1/4) * 6
x = -2 + 1.5
x = -0.5
However, -0.5 is not one of the answer options, so there seems to be a mistake in the process or the question as asked does not match with the provided options. The correct approach with the given values and method would result in an x-coordinate not listed in the options A) 0 B) 1 C) 2 D) 3.