Chapter 1: Q7 (page 24)

Postulate 6 is sometimes stated as “Two points determine a line.”
Do three points determine a plane?

Short Answer

Expert verified

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

Step by step solution

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.”

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Postulate 6 is sometimes stated as “Two points determine a line.”
Do three points determine a plane?

Short Answer

Step by step solution

Step 1. State postulate 6.

Step 2. Collinear and non-Collinear points.

Step 3. Justify if three points determine a plane.

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Postulate 6 is sometimes stated as “Two points determine a line.”Do three points determine a plane?

Short Answer

Step by step solution

Step 1. State postulate 6.

Step 2. Collinear and non-Collinear points.

Step 3. Justify if three points determine a plane.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Calculus

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Postulate 6 is sometimes stated as “Two points determine a line.”
Do three points determine a plane?