Q25. - Geometry

Question

a. Are points $R$, $S$, $G$ and $F$ coplanar?

b. Are points $R$, $S$, $G$ and $C$ coplanar?

Step-by-Step Solution

Answer

1. The points $R$, $S$, $G$ and $F$ are coplanar.
2. The points $R$, $S$, $G$ and $C$ are not coplanar.

Part a. Step 1. Observe the diagram.

The given diagram is:

Part a. Step 2. Definition of the coplanar points.

The coplanar points are the points that lie on the same plane.

Part a. Step 3. Determine whether the points R , S , G and F are coplanar on basis of the definition of collinear points.

From the diagram, it can be noticed that:

 

The points $R$, $S$, $G$ and $F$ are coplanar points as the points $R$, $S$, $G$ and $F$ lie on the same plane $RSGF$.

Part b. Step 1. Observe the diagram.

The given diagram is:

Part b. Step 2. Definition of the coplanar points.

The coplanar points are the points that lie on the same plane.

Part b. Step 3. Determine whether the points R , S , G and C are coplanar on basis of the definition of coplanar points.

From the diagram, it can be noticed that:

The points $R$, $S$, $G$ and $C$ are not coplanar points because the points $R$, $S$, $G$ and $C$ do not lie on the same plane.