Let the equations of three lines in a plane be written in the normal form. (Secant - secant theorem) If two secants, and, also cut the circle at and. 1933 GEOMETRIC INTERPRETATION OF SOME FORMULAS 143. And AB c=, BC a=, CA b= Then incentre of triangle 1 2 3 1 2 3,ax bx cx ay by cy a b c a b c + + + + = + + + + See proof at page 184 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … ≥ Rotation of Axes Let (, )x y be the coordinates of point P in xy-coordinate system. Theorems: (Chord theorem) The chord theorem states that if two chords, and, intersect at, then: (Tangent-secant theorem) If a tangent from an external point meets the circle at and a secant from the external point meets the circle at and respectively, then. Intersection of median is called centroid of triangle and can be determined as 1 2 3 1 2 3, 3 3 x x x y y y+ + + + See proof at page 184 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … ≥ Centre of In-Circle (In-Centre) Let ( )1 1,A x y, ( )2 2,B x y and ( )3 3,C x y are vertices of triangle. Distance between two parallel lines : Let the equations of two parallel lines be.
Distance between a point and a line : The distance from a point P (x1, y1) to a line ax + by + c 0 is. These definitions are designed to be consistent with the underlying Euclidean geometry. Then the angle between these two straight lines is. See proof on book at page 182 ……………………………………………………………………………………………………………………………………… ≥ Intersection of Median Let ( )1 1,A x y, ( )2 2,B x y and ( )3 3,C x y are vertices of triangle. In analytic geometry, geometric notions such as distance and angle measure are defined using formulas. 1 2: 1:1k k = then coordinate of C becomes 1 2 1 2, 2 2 x x y y+ + .
The coordinates of the point C dividing the line segment AB in the ratio 1 2:k k are 1 2 2 1 1 2 2 1 1 2 1 2 ,k x k x k y k y k k k k + + + + If C be the midpoint of AB i.e. 2706770 Analytic Geometry Formula Sheet Below are the formulas you may find useful as you work.
#Analytic geometry formulas pdf#
Download Analytics Geometry Cheat Sheet and more Analytical Geometry Cheat Sheet in PDF only on Docsity!1 Introduction to Analytics Geometry Calculus and Analytic Geometry, MATHEMATICS 12 ≥ Distance Formula Let 1 1(, )A x y and 2 2(, )B x y be two points in a plane and d be a distance between A and B then 2 22 1 2 1( ) ( )d x x y y= − + − or 2 21 2 1 2( ) ( )d x x y y= − + − See proof on book at page181 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … ≥ Ratio Formula Let 1 1(, )A x y and 2 2(, )B x y be two points in a plane. analytic geometry formulas pdfAnalytic Geometry Formulas.
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