Overview of Distance, Midpoint, and Slope in a Cartesian Coordinate System

* Classical Concepts in Advance Algebra and Analytical Geometry *

 

 

(+2, +3)

Definition of Distance:  Length between 2 points.

 

Pythagorean Theorem:  a2 + b2 = c2

 

 

D = { (X1-X2)2 + (Y1-Y2)2 }1/2

                                                            (-3, -2)                                   (+2, ­-2)

           

The Square Root of the Sum of the Differences.

 

 

 

 

Definition of Midpoint:  Average Point of 2 Points.

(-2, ­+3)

 

Arithmetic Average:  (N1 + N2)/2

 

 

M = { (X1+X2)/2 , (Y1+Y2)/2 }

            (-2, ­-2)                                   (+3, ­-2)

 

The average of the X and Y coordinate values.

 

 

 

 

           

Definition of Slope:      Rise / Run   or   Slant

(+2, ­+3)

 

Difference of Ys /  Difference of Xs

 

                                   

            m = (Y2 – Y1) / (X2 – X1)

 

            (-2, ­-2)                             (+2, ­-2)

Ratio of Vertical Change to Horizontal Change

 

 

Tom Love                          Malone College                         Fall 2003