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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
The distance between two points in the rectangular coordinate system is calculated with the distance formula derived from the Pythagorean theorem: \[ d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \] where d is the distance, (x1, y1) are the coordinates of the first point and (x2, y2) are the coordinates of the second point.

Step by step solution

01

Understanding the Coordinate System

In a rectangular coordinate system, points are identified by coordinates (x, y). The x-coordinate represents the horizontal position and the y-coordinate represents the vertical position.
02

Introduce the Distance Formula

The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula: \[ d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \] This is derived from the Pythagorean theorem as it calculates the hypotenuse of a right-angled triangle formed by the vertical and horizontal distances.
03

Applying the Distance Formula

To find the distance between two points, subtract the x-coordinates of the two points and square the result, do the same for the y-coordinates, then add the two results together. The square root of this sum gives the distance between the two points.

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