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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.