Q7 - Geometry

Question

Postulate 6 is sometimes stated as “Two points determine a line.”

 

Do three points determine a plane?

Step-by-Step Solution

Answer

Three points can determine a plane if and only if the three points are not in one line, i.e. non-collinear.

Step 1. State postulate 6.

Postulate 6 states that “Two points determine a line”.

Step 2. Collinear and non-Collinear points.

At least two points can determine one line if those points are collinear and at least two lines if the points are non-collinear.

Step 3. Justify if three points determine a plane.

In order to justify, consider the following statement “Do three points determine a plane?” and give reasoning to state if it is true or false:

From Postulate 5, “A plane contains three points not all in one line.”

Therefore, three points can determine a plane if and only if the three points are not in one line.

 

Hence, the answer is “three points can determine a plane if and only if the three points are not in one line, i.e. non-collinear.”