Q24. - Geometry

Question

a. Are points $A$, $D$ and $C$ collinear?

b. Are points $A$, $D$ and $C$ coplanar?

Step-by-Step Solution

Answer

1. The points $A$, $D$ and $C$ are not collinear.
2. The points $A$, $D$ and $C$ are coplanar.

Part a. Step 1. Observe the diagram.

The given diagram is

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

The collinear points are the points that lie on the same line.

Part a. Step 3. Determine whether the points A , D and C are collinear on basis of the definition of collinear points.

From the diagram, it can be noticed that:

The points $A$, $D$ and $C$ are not collinear points as the points $A$, $D$ and $C$ do not lie on the same line.

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 A , D and C are coplanar on basis of the definition of coplanar points.

From the diagram, it can be noticed that:

The points $A$, $D$ and $C$ are coplanar points as the points $A$, $D$ and $C$ lie on the same plane $ABCD$.