Question

to find the distance between two points, you must calculate the square root of the sum of the squares of the differences in the and coordinates. the coordinate system is essential for plotting points and applying the distance formula.

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. So you calculate the square - root of the sum of the squares of the differences in the $x$ and $y$ coordinates.

Step2: Identify coordinate system

The Cartesian (or rectangular) coordinate system is used for plotting points and applying the distance formula.

Answer:

1. $x$; $y$
2. Cartesian (or rectangular)