Question

which of the following statements is not true?
choose the incorrect statement below.
a. the distance between two points is always greater than or equal to zero.
b. the pythagorean theorem is used to derive the distance formula.
c. it is possible for the distance between two points to be negative.
d. for any real numbers x1 and x2, the expression |x2 - x1|^2 is equivalent to the expression (x2 - x1)^2.

Explanation:

Distance is a non - negative quantity representing the separation between two points. The Pythagorean theorem is indeed used in deriving the distance formula. Also, for any real numbers \(x_1\) and \(x_2\), \(\vert x_2 - x_1\vert^2=(x_2 - x_1)^2\) since squaring a number and squaring its absolute value yield the same result. It is impossible for the distance between two points to be negative.

Answer:

C. It is possible for the distance between two points to be negative.