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:

Step1: Analyze ray - line relationship

A ray has one endpoint and extends infinitely in one direction. A line extends infinitely in both directions. Ray OX and ray OY have endpoint O and extend towards X and Y respectively, but they do not lie on line XY as their starting - point is O. So, "Line XY contains ray OX and ray OY" is false.

Step2: Analyze line - segment relationship

A line contains all the points between any two points on it. Segment YX is part of line XY as a line contains all the segments with endpoints on it. So, "Line XY contains segment YX" is true.

Step3: Analyze segment identity

\(\overline{CA}\) and \(\overline{AC}\) have the same two endpoints A and C. They are the same segment, just named in reverse - order. So, "\(\overline{CA}\) and \(\overline{AC}\) are different segments" is false.

Step4: Check ray existence

There are no points B and A in the diagram such that ray BA can be formed. So, "Ray BA exists in the diagram" is false.

Step5: Check ray existence

Ray YX starts at Y and extends towards X. Since points X and Y are in the diagram, ray YX exists. So, "Ray YX exists in the diagram" is true.

Answer:

Line XY contains segment YX, Ray YX exists in the diagram.