L07 - Lecture 7 Part I Section 1.1 Rectangular Coordinates...

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Unformatted text preview: Lecture 7, Part I: Section 1.1 Rectangular Coordinates Def. The rectangular or Cartesian coordi- nate system is formed by coordinate axes: horizontal u1D465-axis and vertical u1D466-axis. The origin is the point of intersection of coordinate axes. the axes divide the coordinate plane or u1D465u1D466- plane into four quadrants . IV I III II Each point u1D443 in the u1D465u1D466-plane corresponds to an ordered pair ( u1D465,u1D466 ) of real numbers called the coordinates of u1D443 . To plot u1D443 = ( u1D465,u1D466 ): u1D465-coordinate: directed distance of the point from the u1D466-axis u1D466-coordinate: directed distance of the point from the u1D465-axis ex. Plot u1D443 1 = ( − 3 , − 2) and u1D443 2 = (1 , 3). ex. Locate all points which are 2 units above the u1D465-axis. In which quadrant(s), if any, do they lie? ex. Locate all points with u1D465-coordinate 0. Pythagorean Theorem For a right triangle with hypotenuse of length u1D450 and sides of lengths u1D44E and u1D44F , we have u1D44E 2 + u1D44F 2 = u1D450 2 . NOTE: The converse of the theorem is also true. That is, if u1D44E 2 + u1D44F 2 = u1D450 2 , then the triangle is a right triangle. Distance Formula The distance between two points u1D434 = ( u1D465 1 ,u1D466 1 ) and u1D435 = ( u1D465 2 ,u1D466 2 ) is given by u1D451 ( u1D434,u1D435 ) = B A ex. If u1D443 = ( − 2 , 4) and u1D444 = (4 , − 3), find the distance between u1D443 and u1D444...
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L07 - Lecture 7 Part I Section 1.1 Rectangular Coordinates...

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