Q16 - Geometry

Question

State whether it is possible for the figure described to exist. Write yes or no.

Two points lie in a plane X, two other points lie in a different plane Y, and the four points are coplanar but not collinear.

Step-by-Step Solution

Answer

Yes, it is possible that two points lie in a plane , two other points lie in a different plane , and the four points are coplanar but not collinear.

Step 1. Draw a plane X having two points A and B on it and a plane Y having two points C and D on it.

The figure representing the plane having points  and on it and a plane  having points and  on it is:

Step 2. Draw the plane ABDC.

Construct the plane ABCD.

Step 3. State whether it is possible that two points lie in a plane X, two other points lie in a different plane Y, and the four points are coplanar but not collinear.

From the above diagram, it can be noticed that the two points A and B lie on the plane X and the two points C and D lie on the plane Y and the points A, B, C, and D are coplanar that is lie on the same plane ABCD but they are not collinear.

Therefore, it is possible that two points lie in a plane X, two other points lie in a different plane Y, and the four points are coplanar but not collinear.