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Coordinate system

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Information about Coordinate system
Education

Published on January 29, 2009

Author: girishsir

Source: authorstream.com

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Coordinate Geometry : Coordinate Geometry Coordinate plane--a two-dimensional surface on which a coordinate system has been set up; invented by Rene Descartes; also called Cartesian plane, graph, coordinate grid. Coordinates--the numbers in an ordered pair that locate a point in the coordinate plane Ordered pair--a pair of numbers, written as (x, y), that represents a point on a coordinate grid Line segment--the part of a line between two points on the line, including the two points Slide 2: X-axis--the horizontal number line on a coordinate grid Y-axis--the vertical number line on a coordinate grid Quadrants : The four parts made by X and Y axis Origin : Intersection of X and Y axis To plot points, always write the ‘x’ value first and then the ‘y’ value. Ex. (2, 3) (3, -1) (-2, 3) (-3, -2) Each of these points represents a point in each of the four quadrants (go through I to IV). Slide 3: X -X - Y Y 1 2 3 4 1- 2- 3- 4 - I Quadrant II Quadrant III Quadrant IV Quadrant 1 2 3 -1 -2 -3 x, y both are positive x is negative y is positive x , y both are negative x is positive y is negative 0 Origin While plotting any points always remember : While plotting any points always remember The first value in the bracket is for x and second value is for y (x, y) The following table shows position of points on coordinate system. x coordinate is also called as abscissa. y coordinate is also called as ordinate. Slide 5: X -X - Y Y 1 2 3 4 -1 -2 -3 -4 I Quadrant II Quadrant III Quadrant IV Quadrant 1 2 3 -1 -2 -3 0 Represent point (2,3) Slide 6: X -X - Y Y 1 2 3 4 -1 -2 -3 -4 I Quadrant II Quadrant III Quadrant IV Quadrant 1 2 3 -1 -2 -3 0 (3, -1) Represent point (3, -1) Slide 7: X -X - Y Y 1 2 3 4 -1 -2 -3 -4 I Quadrant II Quadrant III Quadrant IV Quadrant 1 2 3 -1 -2 -3 0 (-2,3) Represent point (-2,3) Slide 8: X -X - Y Y 1 2 3 4 -1 -2 -3 -4 I Quadrant II Quadrant III Quadrant IV Quadrant 1 2 3 -1 -2 -3 0 (-3,-2) Represent point (-3,-2) Slide 9: 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 X Y -X 0 -Y 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 Parallelogram Plot the following points and state the type of figure formed by it (5,1) ,(1,1), (6,6) and (2,6) Slide 10: 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 X Y -X 0 -Y 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 Square Plot the following points and state the type of figure formed by it (-4,3) ,(1,3), (-4,-2) and (1,-2) Slide 11: 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 X Y -X 0 -Y 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 Scalene Triangle Plot the following points and state the type of figure formed by it (1,3) ,(4,5), and(5,-4) Now let us solve the Equations graphically : Now let us solve the Equations graphically Solve the equation y = 3x Solve the equation x + y = 7 Solve the equation 3x – 5y = 10 Slide 13: 1. Solve equation y = 3x Steps Take any three values of x and find corresponding value of y 1. y = 3x ?y = 3(1) ? y = 3 2. y = 3x y = 3(2) y = 6 3. y = 3x y = 3(-1) y = -3 x y (x,y) 1 3 (1,3) 2 6 (2,6) -1 -3 (-1,-3) After getting these three order pairs plot them on coordinate plane Slide 14: 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 X Y -X 0 -Y 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 (1,3) (2,6) (-1,-3) y = 3x Slide 15: 2. Solve equation x + y = 7 Steps First take x on other side of equation, so that equation becomes y = 7 – x Take any three values of x and find corresponding value of y 1. y = 7 - x ?y = 7 – 1 ? y = 6 2. y = 7 – x y = 7 – 2 y = 5 3. y = 7 – 0 y = 7 y = 7 x y (x,y) 1 6 (1,6) 2 5 (2,5) 0 7 (0,7) Slide 16: 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 X Y -X 0 -Y 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 (2,5) (1,6) (0,7) x + y = 7 Slide 17: 2. Solve equation 3x – 5y = 10 Change the subject of given equation to y in the following way: 5y = 10 – 3x ? 5y = 3x – 10 ? y = Take any three values of x and find corresponding value of y y = 3x - 10 5 ?y = 3(0) - 10 5 ? y = -2 2. y = 3x - 10 5 ?y = 3(5) - 10 5 ? y = 1 3. y = 3x - 10 5 ?y = 3(-5) - 10 5 ? y = -5 x y (x,y) 0 -2 (0,-2) 5 1 (5,1) -5 -5 (-5,-5) 3x – 10 5 Slide 18: 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 X Y -X 0 -Y 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 (5,1) (0,-2) (-5,-5) 3x – 5y = 10 Slide 19: Presented by GIRISH S RAO

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