Question

1. which of the following statements about the distance formula is true?

the distance formula cannot be derived from the pythagorean theorem.
the distance formula can be written correctly in only one way.
the distance formula can be written correctly in several different ways.
the distance formula only applies to points in one dimension.

Explanation:

• The distance formula is derived from the Pythagorean Theorem, so the first statement is false.
• It can be rewritten equivalently (e.g., swapping the order of coordinates under the square root, or extending to higher dimensions), so it is not limited to one form, making the second statement false.
• The formula applies to 2D, 3D, and higher-dimensional points, not just 1D, so the fourth statement is false.
• The third statement is true because the formula can be rearranged or extended while remaining mathematically correct.

Answer:

C. The distance formula can be written correctly in several different ways.