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"

A line XY does not contain rays OX and OY because the endpoints of OX and OY are O and they are not part of the set - up of 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 just the part of line XY between points Y and X. 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 points B and A in the diagram, and a ray with endpoint B extending towards A can be formed. So this statement is true.

Step6: Analyze "Ray YX exists in the diagram"

There is no indication in the diagram that there is a ray with endpoint Y extending towards X. So this statement is false.

Answer:

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