Final answer:
Using the section formula, the y-value for the point that divides the line segment CD in a ratio of 4:1 is calculated to be 2, which does not match any of the provided options. This suggests there may be an issue with the question or answer choices given.
Step-by-step explanation:
To find the y-value for the point that divides the line segment CD into a ratio of 4:1, we can use the section formula. For two points C (x1, y1) and D (x2, y2), if a point P divides CD in the ratio m:n, the coordinates of P are given by:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
In this case, C is (9,6), D is (5,1), and the ratio is 4:1. Using the formula:
x = (4*5 + 1*9) / (4 + 1) = (20 + 9) / 5 = 29/5 = 5.8
y = (4*1 + 1*6) / (4 + 1) = (4 + 6) / 5 = 10/5 = 2
However, none of the given options has the y-value of 2. This suggests a possible error in the provided options or a misinterpretation of the question. Assuming the question and the answer choices are accurate, the answer should be recalculated, or the question should be reviewed for correctness.