Q16WE. - Geometry

Question

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

Two points lie in a plane $\mathbf{X}$, two other points lie in a different plane $\mathbf{Y}$, 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 $X$, two other points lie in a different plane $Y$, 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 $X$ having points $A$ and $B$ on it and a plane $Y$ having points $C$ and $D$ on it is:

Step 2. Draw the plane ABDC.

Construct the plane $ABDC$.

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 lying 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.