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Chapter 1: 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 calculate the distance between two points in a rectangular coordinate system, identify the coordinates of both points. Then, subtract the x-coordinate of the first point from the x-coordinate of the second point and square the result. Do the same for the y-coordinates. Lastly, sum both results and take the square root. This is done by applying the formula d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

Step by step solution

01

Understand the coordinate system

In a rectangular coordinate system, a point is identified by an ordered pair (x, y), where x represents the distance from the origin (the intersection of the x-axis and y-axis) along the x-axis, and y represents the distance from the origin along the y-axis.
02

Identify the two relevant points

The two points that the distance would be measured between are (x_1, y_1), and (x_2, y_2). x_1 and y_1 are the x and y coordinates of the first point, while x_2 and y_2 are the coordinates of the second point.
03

Apply the distance formula

Plug the coordinates of the two points into the distance formula: d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. Start by finding the difference between the x-coordinates, and square it. Do the same for y-coordinates. Add both results, then calculate the square root of the total.

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