Question

the distance formula is derived from which mathematical theorem?
a. binomial theorem
b. pythagorean theorem
c. mean value theorem
d. fundamental theorem of algebra

what is the term for a pair of numbers that represent the position of a point on a coordinate plane?
a. fraction
b. position point
c. ordered pair
d. integer

Explanation:

1. The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ in a coordinate - plane is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, which is derived from the Pythagorean Theorem. The Pythagorean Theorem states that in a right - triangle, $a^{2}+b^{2}=c^{2}$, and we can form a right - triangle with the line segment between two points as the hypotenuse.
2. In a coordinate plane, the position of a point is represented by an ordered pair $(x,y)$ where $x$ is the horizontal coordinate and $y$ is the vertical coordinate.

Answer:

1. b. Pythagorean Theorem
2. c. Ordered pair