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1-6 THE COORDINATE PLANE (p. 43-49) In the coordinate plane, a point is described by an ordered pair of numbers called the x and y coordinates of the point. Example: Sketch the coordinate plane and review the four quadrants, the two axes, and the origin. In what quadrants are the x-coordinates positive? negative? In what quadrants are the y-coordinates positive? negative? If two points are on a horizontal or vertical line, you can find the distance between them by using the Ruler Postulate (use absolute value and subtraction). Example: Find the distance between two points that lie on a horizontal line that goes through -4 on the y axis. Example: Find the distance between two points that lie on a vertical line that goes through 6 on the x axis. If two points do not lie on either a horizontal or vertical line (that is, they lie on a diagonal or slanted line), you can not use simple subtraction to find the distance between them. You must use the Distance Formula to find the distance between these two points. The Distance Formula The distance d between two points A (x1 , y1 ) and B (x 2 , y 2 ) is d (x 2 x 1 ) 2 ( y 2 y1 ) 2 . Example: Find the distance between C (-2,6) and D (6,-2) to the nearest tenth. This will give an approximate answer. Also briefly discuss simplest radical form which will give an exact answer. Do 1 a and b on p. 44. Do 2b on p. 44. To find the coordinate of the midpoint of a segment on a number line, simply find the average or arithmetic mean of the coordinates of the two endpoints. Example: J K -6 13 J and K lie on a number line. Find the coordinate of the midpoint of JK. When you find the coordinates of the midpoint of a segment in the coordinate plane, you use the averaging process twice- once for the x-coordinates and once for the ycoordinates. The Midpoint Formula The coordinates of the midpoint M of AB with endpoints A (x1 , y1 ) and B (x 2 , y 2 ) are the following: x x 2 y1 y 2 M( 1 , ) 2 2 Example: AB has endpoints (8,9) and (-3,-15). Find the coordinates of the midpoint M. Sometimes you may know the coordinates of the midpoint and one endpoint, and you need to find the coordinates of the second endpoint. You still use the midpoint formula to find the coordinates of the other endpoint, but in a slightly different fashion. Example: The midpoint of DG is M (-1,5). One endpoint is D (1,4). Find the coordinates of the other endpoint G. If time, do 4 on p. 45. Have students copy my Distance and/or Midpoint Formula programs from my TI program collection. Homework p. 46-49: 5,7,15,20,23,27,29,41,50,64,65,74,76,78 50. Use the distance formula program to get an answer in grid units. Multiply this answer by 0.1 to convert to miles.