Problem 75 - College Algebra

Question

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

Step-by-Step Solution

Answer

The distance between two points in a rectangular coordinate system can be calculated using the distance formula \(d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\).

Step 1: Understand the Concept

The first step involves understanding what the rectangular coordinate system is. It is a two-dimensional graph with two axes, namely x and y. Every point in the system can be represented as (x, y).

Step 2: Identify the Points

The next step is to identify the two points between which the distance is to be measured. Label these points A and B, with their respective coordinates as (x1, y1) for A and (x2, y2) for B.

Step 3: Apply the distance formula

Using the distance formula, \(d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\), calculate the distance by substituting the values of x1, x2, y1, and y2 from your identified points.

Step 4: Solve the equation

Finally, solve the equation generated in Step 3. This will be your distance between points A and B.