Q6 - Geometry

Question

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

 

Do three points determine a line?

Step-by-Step Solution

Answer

Three points determine a line only if they are collinear points.

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 line.

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

From Postulate 5

“A line contains at least two points.”

Therefore, three points can determine one line if three points are collinear and three lines if the points are non-collinear.

 

Hence, the answer is “three points can determine a line if the three points are collinear and three lines if the points are non-collinear.”