Question

Planes X and Y and points C, D, E, and F are shown.

Vertical plane X intersects horizontal plane Y. Point D is on the left half of plane Y. Point F is on the bottom half of plane X. Point E is on the right half of plane Y. Point C is above and to the right of the planes. Which statement is true about the points and planes?

The line that can be drawn through points C and D is contained in plane Y.
The line that can be drawn through points D and E is contained in plane Y.
The only point that can lie in plane X is point F.
The only points that can lie in plane Y are points D and E.

Answer 1

The line that can be drawn through points D and E is contained in plane Y.

Explanation:

The line passing through points C and D is not necessarily contained in plane Y because point C is described as being above and to the right of the planes, indicating that it may not lie within the intersection of the two planes.

The line passing through points D and E is contained in plane Y because both points D and E are described as being on the left and right halves of plane Y, respectively. Therefore, any line connecting these two points would be contained within plane Y.

The statement "The only point that can lie in plane X is point F" is not true since the description of the points does not indicate any restriction on the possible points that can lie in plane X. Other points could potentially lie in plane X as well.

The statement "The only points that can lie in plane Y are points D and E" is not true either. While points D and E are explicitly mentioned to lie in plane Y, point C is also described as being on the right half of plane Y, indicating that it could also potentially lie in plane Y.