points c, d, and g lie on plane x. points e and f lie on plane y. which statements are true? select three…

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.

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.

Answer

Explanation:

Step1: Recall plane - point relationship

A plane is determined by three non - collinear points. If two points lie in a plane, the line passing through them lies in the plane.

Step2: Analyze each statement

  • For the statement "There are exactly two planes that contain points A, B, and F": Three non - collinear points determine a unique plane, so this is false.
  • For the statement "There is exactly one plane that contains points E, F, and B": Since E and F are in plane Y and B is outside plane Y, there is no single plane that contains all three, so this is false.
  • For the statement "The line that can be drawn through points C and G would lie in plane X": Since C and G lie in plane X, the line through them lies in plane X, so this is true.
  • For the statement "The line that can be drawn through points E and F would lie in plane Y": Since E and F lie in plane Y, the line through them lies in plane Y, so this is true.
  • For the statement "The only points that can lie on plane Y are points E and F": Plane Y contains infinitely many points, not just E and F, so this is false.

Answer:

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.