OCR Advanced FSMQ - Additional Maths

(c) As line L is perpendicular to CD the product of their gradients is −1. ( − 1 3 ) m 2 = − 1 Giving gradient of L = 3 Equation of line L is: y − 1 = 3( x − 0) y = 3 x + 1 Hence 3 x − y + 1 = 0 TAKE NOTE You must show all the working out here. Do not simply change the sign and invert the fraction without explaining why this is done. TAKE NOTE Leaving the equation in the form y = mx  + c (i.e. as y = 3 x + 1) would cost you a mark here as the question asks that the equation be given in the form ax + by + c = 0. Test yourself Answer the following questions and check your answers before moving on to the next topic. 1 The points A , B , C , D have coordinates (1, 0), (4, 1), (−1, 3), (2, 4) respectively. (a) Show that lines AB and CD are parallel. (b) Find the equation of AB in the form ax + by + c = 0. 2 The points A and B have coordinates (−7, 4) and ( k , −1) respectively. (a) If the gradient of AB is − 1 2 , find the value of the constant k . (b) The line BC is perpendicular to AB . Find the equation of line BC . 3 The points A , B , C have coordinates (−3, 2), (1, 6), (6, 1). (a) Show that AB is perpendicular to BC . (b) Find the length of AB and the length of BC . (c) Find the value of tan  AĈB in the form a b . 4 A line has the equation 3 x + 2 y = 5. Another line is drawn having the same gradient and passing through the point (3, 4). Find the equation of this line. 2 Coordinate geometry 140