OCR Advanced FSMQ - Additional Maths

5 The points P and Q have coordinates (−4, 0) and (0, 2) respectively. (a) Find the equation of the line PQ . (b) Find the equation of the line perpendicular to PQ through its mid-point. 6 The points P , Q , R have coordinates (1, 0), (3, 5), (−2, 6) respectively. (a) Find the gradient of line PQ . (b) Find the equation of line PQ and simplify your answer. (c) S is the point such that PQRS forms a parallelogram. State the gradient of line RS and use this to find the equation of the line RS . (d) If the equation of line SP is 5 y + x = 1, find the coordinates of point S . 7 The coordinates of the points A , B , C and D are (2, −5), (6, −7), (9, −4) and (5, −2) respectively. (a) Find the gradient of the line joining points A and B . (b) Prove that the lines AB and DC are parallel. (c) Prove that the lines AB and DC are the same length. (d) Prove that the quadrilateral ABCD is a parallelogram. 8 A (4, 2) and B (1, 5) are two points. (a) Find the coordinates of the mid-point, M of AB . (b) Find the gradient of the line joining A and B . (c) The line from point M passes through the point C (4, 5). Prove that the lines AB and MC are perpendicular. (d) Find the equation of the line MC . 9 The line PQ has equation 2 x + 3 y = 5. The point R has coordinates (3, 3). (a) Find the gradient of line PQ . (b) A line is drawn which passes through R and is parallel to PQ . If this line crosses the y -axis at point S , find the coordinates of S . 10 The line AB has equation 4 x + 5y = 10. (a) Find the gradient of AB . (b) Prove that the point C (−5, 6) lies on AB . (c) Find the equation of the line through C which is at right angles to AB . 6 Coordinate geometry of straight lines 141