MAT 121 Lecture Notes - Hypotenuse, Abscissa And Ordinate, Hyperbola
Document Summary
The position of a point in a plane can be described using cartesian, or rectangular, co- ordinates. In the cartesian system we fix an origin, a point (cid:1841), and then take two lines which are perpendicular to each other passing through (cid:1841). The (cid:1876)-axis is horizontal, and the (cid:1877)-axis is vertical. Suppose that we want to find the distance between two points (cid:1827)((cid:883)(cid:481)(cid:885)) and (cid:1828)((cid:886)(cid:481)(cid:887)). We can start by drawing a sketch as shown. We join (cid:1827) and (cid:1828) to form a line segment. Then to find the length (cid:1827)(cid:1828) we use pythagoras". So we make (cid:1827)(cid:1828) the hypotenuse of an appropriate right-angled triangle(cid:1827)(cid:1828)(cid:1829). This means that (cid:1829) must be the point ((cid:886)(cid:481)(cid:885)). The distance (cid:1827)(cid:1829) is (cid:886)(cid:3398)(cid:883)(cid:3404)(cid:885), and the distance (cid:1828)(cid:1829) is (cid:887)(cid:3398)(cid:885)(cid:3404)(cid:884). So, substituting the values for (cid:1827)(cid:1829) and (cid:1828)(cid:1829), we obtain ((cid:1827)(cid:1828))(cid:2870)(cid:3404) ((cid:885))(cid:2870)(cid:3397)((cid:884))(cid:2870)(cid:3404)(cid:891)(cid:3397)(cid:886)(cid:3404) (cid:883)(cid:885) (cid:481) Let us take two general points (cid:1827)((cid:1876)(cid:2870)(cid:481)(cid:1877)(cid:2870)) and (cid:1828)((cid:1876)(cid:2870)(cid:481)(cid:1877)(cid:2870)) as shown.
