Cartesian
Coordinate System
Objectives:
O Use the Distance Formula
O Use the Midpoint Formula
A (-3,1)
B (-2,3)
C (6,4)
Distance Between
Two Points
Distance Formula
O The distance formula between two points
P1 = (x1 , y1) and P2 = (x2 , y2), denoted by
d(P1,P2), is
d(P1,P2) = (𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
Proof of the Distance Formula
Finding the Distance Between Two Points
O Sample Problem: Find the distance d between the points
(1,3) and (5,6).
Sample Problem
Determine the length of the line segment AB, AC, and
AD using the distance formula.
Midpoint Formula
O The midpoint M = (x,y) of the line segment
from P1 = (x1 , y1) to P2 = (x2 , y2), is
M = (x , y) = (
𝒙𝟏 + 𝒙𝟐
𝟐
,
𝒚𝟏 + 𝒚𝟐
𝟐
)
Finding the Midpoint of a Line Segment
O Sample Problem: Find the midpoint of a line segment
from P1 = (-5,5) to P2 = (3,1)
Seatwork!
1. Find the midpoint of line segment from P1 =
(4,5) to P2 = (-2,-3). Plot the points P1 and P2
and their midpoint.