mac1105_lecture10_1

# mac1105_lecture10_1 - L10 Rectangular Coordinates Graphs of...

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91 L10 Rectangular Coordinates; Graphs of Equations The Rectangular Coordinate System is formed by the x axis and y axis. A plane with the rectangular coordinate system is called the coordinate plane or xy - plane . This plane has four quadrants: For each point P in the xy - plane , there is a corresponding ordered pair ( , ) x y , where x and y are called coordinates of P , and we write ( , ) P xy = . Example : Determine the quadrant(s) in which ( , ) x y is located if 0 x < and 0 y < 2 x > and 3 y =

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92 Distance Formula The distance between two points 11 1 (, ) P xy = and 22 2 ) P = , denoted by 12 ) dPP , is 2 1 2 1 ) ( ) ( ) x x y y =− + . Note : 1) ) 0 2) ) 0 = if and only if P P = 3) 21 ) ( , ) = Midpoint A point M on the line segment with endpoints 1 P and 2 P is called the midpoint if ) ( , ) dPM dMP = .
93 Midpoint Formula : The midpoint M of the line segment with the endpoints 11 1 (, ) P xy = and 22 2 ) P = is 12 , x y M + + ⎛⎞ = ⎜⎟ ⎝⎠ . Example : Given two points ( 2, 5) and (4,6), find the midpoint of the line segment joining them. Find the distance between the midpoint and the origin.

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mac1105_lecture10_1 - L10 Rectangular Coordinates Graphs of...

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