Cartesian Coordinate System

advertisement
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.
Download
Random flashcards
State Flags

50 Cards Education

Countries of Europe

44 Cards Education

Art History

20 Cards StudyJedi

Sign language alphabet

26 Cards StudyJedi

Create flashcards