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College Geometry, Formula sheet If A = (a1 , a2 ) and B = (b1 , b2 ) are two given points, then the distance of A and B is p d(A, B) = (b1 − a1 )2 + (b2 − a2 )2 Equations of the line: • If A = (a1 , a2 ) and B = (b1 , b2 ) are points on the line l, then the equation of l is l : (b2 − a2 )x − (b1 − a1 )y = (b2 − a2 )a1 − (b1 − a1 )a2 • If A = (a1 , a2 ) is a point on the line l and v = (v1 , v2 ) is the direction of l, then the equation of l is l : v2 x − v1 y = v2 a1 − v1 a2 • If A = (a1 , a2 ) is a point on the line l, and n = (n1 , n2 ) is the direction perpendicular to l, then the equation of l is l : n1 x + n2 y = n1 a1 + n2 a2 If v = (v1 , v2 ) is the direction of the line l, and n = (n1 , n2 ) is the direction perpendicular to l, then v1 n1 + v2 n2 = 0, that is (v1 , v2 ) = (−n2 , n1 ). Suppose that l1 = a1 x + b1 y = c1 and l2 = a2 x + b2 y = c2 are two lines. • l1 and l2 are parallel is and only if a1 b2 − a2 b1 = 0 • l1 and l2 are perpendicular if and only if a1 b1 + a2 b2 = 0 The equation of the circle with center C = (c1 , c2 ) and radius R is c : (x − c1 )2 + (y − c2 )2 = R2