Question

Find the distance between each pair of points. $$(1,-2),(-3,1)$$

   Find the distance between each pair of points.
$$(1,-2),(-3,1)$$

Geometry

Cindy J. Boyd, Jerry… 1st Edition

Chapter 6, Problem 53

Instant Answer

Solved by Expert Lauren Shelton

10/08/2020

Step 1

The distance formula is given by: \[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\] where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points. Show more…

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Find the distance between each pair of points. $$(1,-2),(-3,1)$$

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Key Concepts

Cartesian Coordinate System

The Cartesian coordinate system allows us to locate points in space using ordered pairs (or tuples in higher dimensions). It is fundamental in analytic geometry because it provides a framework for defining distances and angles between points using numerical coordinates.

Pythagorean Theorem

The Pythagorean Theorem is a principle in geometry that relates the lengths of the sides of a right triangle. It forms the basis of the distance calculation in the coordinate plane by treating the difference in x-coordinates and y-coordinates as the legs of a right triangle.

Distance Formula

The Distance Formula is a direct application of the Pythagorean Theorem in the context of the Cartesian coordinate system. It calculates the distance between two points by taking the square root of the sum of the squares of the differences of their coordinates, providing a method to measure the straight line distance between any two points.

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