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Math 102 2.1 "Coordinate Geometry" Objectives: * Find the distance between two points on a number line and the rectangular coordinate system. * Find the mindpoint of a line segment in the rectangular system. The general formula that we can use to …nd the coordinate of a point between x1 to x2 is x = x1 + Example 1: (Finding coordinates of intermediate points) Find the coordinate of the point located three-fourths of the distance from a (x2 b x1 ) 2 to 14 on a number line. Rectangular Coordinate system The idea of associating an ordered pair of numbers with points on a grid is attributed to the 17th century French mathematician Rene Descartes. Such a grid is called: Rectangular (Cartesian) Coordinate System. The point where the axes intersect is called . and divide it into The two axes form a four regions called : Every point on a coordinate plane can be identi…ed by an of real numbers x and y;written as: : Distance Between Two Points Distance Formula: The distance d between two points with coordinates (x1 ; y1 ) and (x2 ; y2 ) ; is given by . Example 2: (Using the distance formula) Use the distance formula to verify that the points ( 2; 7) ; (2; 1) ; and (4; 2) lie on a straight line. y x Page: 1 Notes by Bibiana Lopez College Algebra by Kaufmann and Schwitters 2.1 Points of Division of a Line Segment Earlier in this section we discussed the process of …nding the coordinate of a point on a number line, given that it is located somewhere between two other points on the line. This same type of problem can occur in the xy plane. Example 3: (Finding the distance between two points in the coordinate system) Find the coordinate of the point P , which is …ve-sixths of the distance from ( 7; 2) to ( 1; 4) : y x Midpoint Formula: The midpoint of a line segment with endpoints (x1 ; y1 ) and (x2 ; y2 ) is the point with coordinates: Example 4: (Using the midpoint formula) Find the coordinates of the midpoint of the line segment determined by the points ( 5; 2) and ( 1; 6) : Page: 2 Notes by Bibiana Lopez