Problem 76 - 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

To find the distance between two points in the rectangular coordinate system, use the distance formula \(d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\). Subtract the x and y coordinates of the two points, square these values, sum them and take the square root of the result.

Step 1: Understanding The Rectangular Coordinate System

The rectangular coordinate system, otherwise known as the Cartesian coordinate system, is a 2-Dimension system where each point is uniquely determined by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, typically measured in the same unit of length.

Step 2: Identification of The Points

The next step is to identify the two points. Let's say the points are A (x1, y1) and B (x2, y2). Note the coordinates of these two points, where x1, y1 are the coordinates of point A and x2, y2 are coordinates of point B.

Step 3: Using The Distance Formula

When two points A and B are given in the rectangular coordinate system, the distance between them can be found using the distance formula. This formula is derived from the Pythagorean theorem and is given by \(d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\). Subtract the x-coordinate of point A from the x-coordinate of point B and square the result. Do the same for the y-coordinates. Then add these squared values and find the square root of this sum to get the distance.