Brianna is solving a directed line segment question. Part of the problem reads: Y lies on segment XZ such that the ratio of XY to XZ is 1:5. What k value should Brianna use when she solves the problem?

⅕

Step-by-step explanation:

Given that points X, Y, and Z are collinear, and X is said to partition segment XZ in the ratio XY to XZ = 1:5, it means that segment XY = ⅕ of XZ. That is XY/XZ = ⅕

See attachment below to understand how point Y divides segment XZ.

Therefore, the k value Brianna would use when solving the problem should be the fraction, ⅕.

k value = XY/XZ = 1/5