Question

1. what is the distance formula used for calculating the distance between two points on a coordinate plane? a. distance = √((x₂ - x₁)²+(y₂ - y₁)²) b. distance = (x₂ - x₁)²+(y₂ - y₁)² c. distance = √((x₂ + x₁)²+(y₂ + y₁)²) d. distance = (x₂ - x₁)+(y₂ - y₁)

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ in a coordinate - plane is derived from the Pythagorean theorem and is given by $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. This formula calculates the length of the straight - line segment connecting the two points. Options B, C, and D do not correctly represent the distance formula. Option B is missing the square - root, option C has incorrect addition inside the square - root for the $x$ and $y$ coordinates, and option D is a simple sum of differences without squaring and square - rooting as required by the Pythagorean theorem.

Answer:

A. Distance = $\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$