Question

points c, d, and g lie on plane x. points e and f lie on plane y. which statements are true? select three options. there are exactly two planes that contain points a, b, and f. there is exactly one plane that contains points e, f, and b. the line that can be drawn through points c and g would lie in plane x. the line that can be drawn through points e and f would lie in plane y. the only points that can lie on plane y are points e and f.

Explanation:

1. Three non - collinear points determine a unique plane. Points A, B, and F do not necessarily determine exactly two planes, so the first statement is false.
2. Points E, F, and B are not collinear, but there is not exactly one plane that contains them as they can be part of different planes in 3 - D space, so the second statement is false.
3. Since points C and G lie on plane X, the line through C and G lies in plane X according to the property that if two points lie in a plane, the line joining them lies in the same plane.
4. Since points E and F lie on plane Y, the line through E and F lies in plane Y according to the property that if two points lie in a plane, the line joining them lies in the same plane.
5. Points E and F are not the only points that can lie on plane Y as there are infinitely many points on a plane.

Answer:

C. The line that can be drawn through points C and G would lie in plane X.
D. The line that can be drawn through points E and F would lie in plane Y.