Question

question 9 of 10
the distance formula is derived from the pythagorean theorem.
a. true
b. false

Explanation:

The distance formula in a coordinate plane for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\). When we derive the distance formula, we consider the horizontal distance \(\vert x_2 - x_1\vert\) and vertical distance \(\vert y_2 - y_1\vert\) as the legs of a right - triangle, and the distance between the two points as the hypotenuse. So, the distance formula is derived from the Pythagorean theorem.

Answer:

A. True