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# Weeks 1 & 2 of Analytic Geometry MATH 1325 - 001

UTA

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This 2 page Bundle was uploaded by Haley Kincaid on Monday February 1, 2016. The Bundle belongs to MATH 1325 - 001 at University of Texas at Arlington taught by Farid Derisavifard in Fall 2015. Since its upload, it has received 57 views. For similar materials see ANALYTIC GEOMETRY in Mathematics (M) at University of Texas at Arlington.

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Date Created: 02/01/16

1. Plane Analytic Geometry 1.1.The Cartesian System: numbering system used to identify points on a 2 dimensional plane. If 2 points are on the same line they are considered I I II IV collinear. Theorem 1.1: The distance between two points P & P i1 equ2l to √ (x2-x1) +( y 2y 1 2 1.2.If 3 points (A, B, & P) lie on the same line and P is a point on line AB the coordinates of P will be: x= x +r(x 1x ) 2 1 & y=y +1(y +y2) 1 Where r= the proportional distance from A to B point. If P is the midpoint AB, then the coordinates of P are x=(x 1x )22 & 1.3. y=(y +1 )22 1.4.Inclination Angle: the measure of the smallest nonnegative angle. For this lesson ө represents the inclination angle. Slope (m): of a line is he tangent o the inclination so m= tanө A line through P &1P 2 where x ≠x1has2slope m= (y2−y 1)x −x2) 1 If two lines are parallel their slopes will be equal. o o If two lines are perpendicular, then ө =ө 190 2 & ө 1ө 290 1.5.Parallel & Perpendicular lines: the lines l & 1 wit2 slopes m & m , 1 2 respectively are a) parallel or coincident if and only if m =m1 2 b) perpendicular if m m 1-12 Eg. 1 tan a = (tanө -2anө )1(1+tanө tanө1) 2 1.6.Angles from one line to another: cf l & l1are 2on-perpendicular lines with slopes m & 1 , re2pectively and “a” is anb angle from l to l , t1en 2 tan a ө = (m 2m )÷11+m m ) 1 2 Theorem 1.6: If one of the lines (l ) 1s vertical a o it has no slope but it does have an inclination of 90 so tan a = tan(ө+90 )=cot ө= -(1÷(tanө)) 1.7.Graphs and points of intersection to find the points of intersection between 2 graphs solve the first equation for y and in the second replace y with your 2 2 solution. Eg. x +y =25 & x+y=2 x +(2-x) =25 2 Eg. l2 l 2x - 1 1 4x-21=0 And a 2 −b± b √4ac simply plug into the quadratic equation. x= 2a Ө Ө 1 2

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