Question

a. what is the correct formula for finding the distance between two points?

Explanation:

Step1: Recall distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a two - dimensional plane is derived from the Pythagorean theorem. If we consider the horizontal distance between the two points as \(|x_2 - x_1|\) and the vertical distance as \(|y_2 - y_1|\), then by the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the distance between the two points, \(a = |x_2 - x_1|\) and \(b=|y_2 - y_1|\).
So the distance formula \(d=\sqrt{(x_2 - x_1)^{2}+(y_2 - y_1)^{2}}\)

Answer:

The correct formula for finding the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^{2}+(y_2 - y_1)^{2}}\)