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# Coll Alg Bus MATH 1090

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This 2 page Class Notes was uploaded by Miss Noel Mertz on Monday October 26, 2015. The Class Notes belongs to MATH 1090 at University of Utah taught by Staff in Fall. Since its upload, it has received 42 views. For similar materials see /class/229945/math-1090-university-of-utah in Mathematics (M) at University of Utah.

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Date Created: 10/26/15

Math 1090001 Spring 2001 The Cartesian Plane Friday Jan 12 2001 l The Cartesian Plane is a standard graphical representation of R2 the set of ordered pairs of real numbers 0 The Cartesian Plane has a pair of mutually perpendicular coordinate axes Usually these two axes are drawn horizontally and vertically as in the diagram below 0 The point of intersection of these two axes is called the origin 0 The arrow on each axis indicates the direction of increase of the coordinate of that axis Usually we give names to the axes For the discussion below we will call the horizontal axis the xaxis and the vertical one the yaxis 0 Each point in the Plane determines an ordered pair of real numbers and vice versa as follows WNE th 93 Suppose a point P on the plane is given Draw a horizontal and vertical line through P Denote the intersection of this horizontal line with the yaxis the vertical axis by B and denote the inter section of the vertical line with the xaxis the horizontal axis by A We now de ne the ycoordinate denoted by yp of the point P to be the signed distance from the origin to the point A Similarly we de ne the xcoordinate denoted by 95p of P to be the signed distance from the origin to the point B See the diagram below Now we associate to the point P 7 which is in the Cartesian Plane 7 to the ordered pair 95p yp of real num eI S Conversely given any ordered pair a b we assoicate to it the point in the Plane with xcoordinate a and ycoordinate 32 413 1r 7 7 7 7 7 7 7 7 7 7 Plt gtxpyp 0ltyp l l l l l l A 9 x xpgt04gt 7aem oaew The Cartesian Plane Math 1090001 Spring 2001 Friday Jan 12 2001 2 Exercises 1 a Plot the points 74711 and 5 7 b Draw a line through the two points c Which of the following points also lie on the line 72 77 73 76 71 74 0 73 2 3 3 3 11 4 6 2 a Plot the points 75 73 73 71 711 3 5 5 7 7 9 b Draw a line through the plotted points and list several other points on the line c Express the relation between the x and ycoordinates of each point on the line in a verbal statement d Express the same relation in the form y e Will this line pass through the point 7103 7102 Give a reason for your anwser 3 a Plot each of the following pairs of points locate the midpoint of the line segment joining the pair of points and determine the coordinates of each midpoint i 0 0 410 ii 0 0 762 iii 71 3 311 iv 7273 65 v 75 74 79 72 vi 7271 710 79 b How is the xcoordinate of the midpoint related to the xcoordinates of the given endpoints What about the ycoordinate c Without plotting determine the coordinates of the midpoint of the line segment joining the points 13 and l d 197 What is the midpoint of the line segment joining the points x1 y1 and 952 y

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