Analytic Geometry - Whitman College

1 Analytic GeometryMuch of the mathematics in this chapter will be review for you. However, the exampleswill be oriented toward applications and so will take some the (x, y) coordinate system we normally write thex-axis horizontally, with positivenumbers to the right of the origin, and they-axis vertically, with positive numbers abovethe origin. That is, unless stated otherwise, we take rightward to be the positivex-direction and upward to be the positivey-direction. In a purely mathematical situation,we normally choose the same scale for thex- andy-axes. For example, the line joining theorigin to the point (a, a) makes an angle of 45 with thex-axis (and also with they-axis).In applications, often letters other thanxandyare used, and often different scales arechosen in the horizontal and vertical directions. For example, suppose you drop somethingfrom a window, and you want to study how its height above the ground changes fromsecond to second.

160miles from Seattle. Tofind the t-intercept, set 0 = −50t+160, so thatt = 160/50 = 3.2. The meaning of the t-intercept is the duration of your trip, from the start until you arrive in Seattle. After traveling 3 hours and 12 minutes, your distance y from Seattle will be 0. Exercises 1.1. 1.

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  Geometry, Analytics, Thatt, Analytic geometry

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