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Chapter 1: Q7 (page 24)

Postulate 6 is sometimes stated as 鈥淭wo points determine a line.鈥�

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

01

Step 1. State postulate 6.

Postulate 6 states that 鈥淭wo points determine a line鈥�.

02

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.

03

Step 3. Justify if three points determine a plane.

In order to justify, consider the following statement 鈥淒o three points determine a plane?鈥� and give reasoning to state if it is true or false:

From Postulate 5, 鈥淎 plane contains three points not all in one line.鈥�

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

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

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