Download Rectangular Coordinate system Distance Between Two Points

Math 102
2.1 "Coordinate Geometry"
Objectives:
*
Find the distance between two points on a number line and the rectangular coordinate system.
*
Find the mindpoint of a line segment in the rectangular system.
The general formula that we can use to …nd the coordinate of a point between x1 to x2 is x = x1 +
Example 1: (Finding coordinates of intermediate points)
Find the coordinate of the point located three-fourths of the distance from
a
(x2
b
x1 )
2 to 14 on a number line.
Rectangular Coordinate system
The idea of associating an ordered pair of numbers with points on a grid is attributed to the 17th century French
mathematician Rene Descartes. Such a grid is called: Rectangular (Cartesian) Coordinate System.
The point where the axes intersect is called
.
and divide it into
The two axes form a
four regions called
:
Every point on a coordinate plane can be identi…ed by an
of real numbers x and y;written as:
:
Distance Between Two Points
Distance Formula:
The distance d between two points with coordinates (x1 ; y1 ) and (x2 ; y2 ) ;
is given by
.
Example 2: (Using the distance formula)
Use the distance formula to verify that the points ( 2; 7) ; (2; 1) ; and (4; 2) lie on a straight line.
y
x
Page: 1
Notes by Bibiana Lopez
College Algebra by Kaufmann and Schwitters
2.1
Points of Division of a Line Segment
Earlier in this section we discussed the process of …nding the coordinate of a point on a number line, given that it is
located somewhere between two other points on the line. This same type of problem can occur in the xy plane.
Example 3: (Finding the distance between two points in the coordinate system)
Find the coordinate of the point P , which is …ve-sixths of the distance from ( 7; 2) to ( 1; 4) :
y
x
Midpoint Formula:
The midpoint of a line segment with endpoints (x1 ; y1 ) and (x2 ; y2 )
is the point with coordinates:
Example 4: (Using the midpoint formula)
Find the coordinates of the midpoint of the line segment determined by the points ( 5; 2) and ( 1; 6) :
Page: 2
Notes by Bibiana Lopez