Question

which statements are true? check all that apply. line xy contains ray ox and ray oy. line xy contains segment yx. $overline{ca}$ and $overline{ac}$ are different segments. ray ba exists in the diagram. ray yx exists in the diagram.

Explanation:

1. A line extends infinitely in both directions. A ray has one - endpoint and extends infinitely in one direction. A line does not contain rays with a different endpoint (O in this case), so "Line XY contains ray OX and ray OY" is false.
2. A line contains all the segments with endpoints on it. So, line XY contains segment YX as a part of it, which is true.
3. $\overline{CA}$ and $\overline{AC}$ represent the same segment as the order of naming endpoints for a segment does not matter, so this statement is false.
4. There is no point B on the diagram to form ray BA, so this statement is false.
5. There is no point Y on the diagram such that a ray YX can be formed starting from Y and passing through X, so this statement is false.

Answer:

Line XY contains segment YX.