OCR Advanced FSMQ - Additional Maths

Progress check 15 Find the equation of the line parallel to the line 4 x − 3 y = 10 and passing through the point (−3, 2). 16 The points A , B and C have coordinates (1, 1), (3, 3) and (6, 0) respectively. (a) Find the gradients of lines AB and BC . (b) Prove that lines AB and BC are perpendicular to each other. 17 The points P and Q have coordinates (0, 6) and (4, 0) respectively. (a) Find the equation of the line PQ . (b) Find the equation of the line perpendicular to PQ through its mid-point. 18 Here is an equation of a straight line: y = 6 x − 5 Say whether each of the following points lies on the straight line: (a) (1, 1) (b) (0, −5) (c) (2, 4) (d) ( 1 2 , −2) (e) (−1, 1) 19 By substituting x = 0 into each of these equations, determine the y -coordinate of the point where the line cuts the y -axis: (a) y = 4 x −1 (b) y = 3 x + 5 (c) 4 x − 2 y = 0 (d) 5 y − x = 2 (e) 2 x + y −1 = 0 (f) y − x − 3 = 0 20 By substituting y = 0 into each of these equations, determine the x -coordinate of the point where the line cuts the x -axis: (a) y = 4 x + 2 (b) y = −3 x +15 (c) 3 x + 2 y = 12 (d) 5 y − x = 9 (e) 5 x − 7 y = 25 (f) x − y + 7 = 0 (g) 5 x − 3 y − 10 = 0 The point (−1, 1) lies on the straight line because when the x -coordinate is substituted into the equation we obtain: 2 y − 5(−1) = 7 2 y + 5 = 7 2 y = 2 y = 1 Now as this is the y -coordinate of the point (−1, 1), we can say the point lies on the line. 6 Coordinate geometry of straight lines 135