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: Recall line - ray - segment definitions

A line extends infinitely in both directions, a ray has one endpoint and extends infinitely in one direction, and a segment has two endpoints.

Step2: Analyze "Line XY contains ray OX and ray OY"

Ray OX starts at O and goes towards X, ray OY starts at O and goes towards Y. A line XY passing through O does not contain these rays as their starting - point O is not on the line XY in the way described. So this statement is false.

Step3: Analyze "Line XY contains segment YX"

A line contains all the points between any two points on it. Segment YX is a part of line XY. So this statement is true.

Step4: Analyze "CA and AC are different segments"

A segment is defined by its two endpoints. CA and AC have the same two endpoints A and C, so they are the same segment. This statement is false.

Step5: Analyze "Ray BA exists in the diagram"

There are no points B and A in the correct order (starting from B and going towards A) in the given diagram to form ray BA. So this statement is false.

Step6: Analyze "Ray YX exists in the diagram"

Ray YX starts at Y and goes towards X. Since there is a line XY in the diagram, ray YX exists. This statement is true.

Answer:

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