Problem 75 - Precalculus Essentials

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 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 1: 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.

Step 2: 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.

Step 3: 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.