Question

if we are given coordinates which formula should we use to find the distance?

(distance formula)

(pythagoreans theorem)

Explanation:

Step1: Understand the problem

We need to determine the formula for distance given coordinates.

Step2: Recall the distance formula

The distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) is specifically for finding the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) in a coordinate - plane. The Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) is a general formula for right - triangles. When we consider the horizontal and vertical differences between two points \((x_2 - x_1)\) and \((y_2 - y_1)\) as the legs of a right - triangle (analogous to \(a\) and \(b\) in the Pythagorean theorem), the distance \(d\) between the two points is the length of the hypotenuse (analogous to \(c\)). But the distance formula is the direct application for coordinate - based distance calculation.

Answer:

The formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) (Distance Formula) should be used.