Question

1. the distance formula is derived from which mathematical theorem?

a. fundamental theorem of algebra
b. mean value theorem
c. pythagorean theorem
d. binomial theorem

Explanation:

The distance formula calculates the straight-line distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) as \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\), which is directly derived from the Pythagorean Theorem (\(a^2 + b^2 = c^2\)) by treating the horizontal and vertical differences between the points as the legs of a right triangle, and the distance as the hypotenuse.

Answer:

c. Pythagorean Theorem