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Chapter 2: Problem 75

In your own words, describe how to find the distance between two points in the rectangular coordinate system.

Short Answer

Expert verified
To find the distance between two points in a rectangular coordinate system, understand the distance formula, identify the coordinates of both points, substitute these coordinates into the formula, calculate the square differences, add together these squared differences, and finally calculate the square root of the result to get the distance. It is necessary to remember the distance will always be a positive real number.

Step by step solution

01

Understand the problem and the formula

Knowing that it is being asked to find the distance between two points in the rectangular coordinate system, using the distance formula which is \( \sqrt{{(x2 - x1)^2 + (y2 - y1)^2}} \). The 'x' and 'y' here represent points on a 2D plane and the numerical indices represent different points. For example, x1 might represent the x-coordinate of the first point, y1 the y-coordinate of the first point, x2 the x-coordinate of the second point, and so on.
02

Identify the coordinates

Assume you have two points A and B. The coordinates for A are represented as (x1, y1) and those for B are (x2, y2). It is important to know which pair belongs to which point as it affects the calculation.
03

Apply the formula

Substitute the values of the coordinates into the formula. The differences between the 'x' coordinates (x2 - x1) and the 'y' coordinates (y2 - y1) are calculated and squared. This is a reflection of the Pythagorean theorem where the side lengths of a right triangle are squared. These squared differences are then added together.
04

Calculate the distance

Finally, calculate the square root of the result from the previous step. This will give the distance between the two points on the plane. The final result should be a positive real number as it is a distance.

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