Coordinate Geometry

� Consider the points P( x1, y

1) and Q( x2, y

2) on a x - y plane : y2 � y1 1 . m � : Slope of PQ x � _x

2 .

2 1 d � ( x � x ) � ( y � y ) : Distance between P and Q

2 2 2 1 2 1

1 2 1 2

3 .

� ^x � ^x , ^y � ^y � �

�: Mid-point of PQ � 2 2 �

� Consider the points P( x1, y1, z

1) and Q( x2, y2, z

2) on a x - y - z plane : 1 . z -axis : The axis perpendicular to the x - y plane 2 .

d � ( x � x ) � ( y � y ) � ( z � z ) : Distance between P and Q

2 2 2 2 1 2 1 2 1

1 2 1 2 1 2

3 .

� ^x � ^x , ^y � ^y , ^z � ^z � �

�: Mid-point of PQ � 2 2 2 �

� Forms of straight lines with slope m and y -intercept c : 1 . y �mx � c : Slope-intercept form 2 . Ax � By �C

� 0 : General form

� Ways to find the x -intercept and the y -intercept of a line : 1 . Substitute y � 0 and make x the subject to find the x -intercept 2 . Substitute x � 0 and make y the subject to find the y -intercept

Voronoi Diagrams

� Elements in Voronoi Diagrams : Site : A given point Cell of a site : A collection of points which is closer to the site than other sites Boundary : A line dividing the cells Vertex : An intersection of boundaries

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