Question

Decide which ONE of the following statements is FALSE.

Answer 1

True or False.

A is true, a line has two points which are the two ends.

Answer 2

Answer: Choice D

Any three points lie on a distinct line

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Explanation:

Let's go through each statement to see which are true, and which are false.

• A) True. A line is uniquely defined by two points. In other words, you need 2 points to form a line.
• B) True. A plane is a flat surface, such as a table top or a piece of paper. The paper is not allowed to bend or curve. The three points cannot all fall on the same line, hence the "non-colinear" condition put in there. If the 3 points were colinear, then infinitely many planes would go through those points. So we make them non-colinear so a unique single plane can be defined.
• C) True. See choice A above.
• D) False. While two points form a single line, that third point may or may not be on that line. If the three points form a single line, then we consider the points colinear. If the points don't all fall on the same line, then we say they are non-colinear. For non-colinear points, a triangle forms. If choice D said "any three colinear points lie on a distinct line", then that statement would be true.

Side note: The spelling of "colinear" is sometimes "collinear" with two "L"s, instead of one. I'm not 100% sure which spelling is more acceptable. I've found sources that have used both.