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