OCR Advanced FSMQ - Additional Maths

6.7 Equations of vertical and horizontal lines Horizontal lines (i.e. lines parallel to the x -axis and including the x -axis) have an equation of the form y = a , so, for example, y = 2, y = −3, y = 0 are all examples of horizontal lines. Vertical lines (i.e. lines parallel to the y -axis and including the y -axis) have an equation of the form x = a , so, for example, x = 1, x = −4, x = 0 are all equations of vertical lines. Here are some examples of lines parallel to the x - or y -axes and their equations. 7 Find the gradient and the intercept on the y -axis for each of the following straight lines: (a) y = 3 x + 2 (b) 2 y = 4 x + 6 (c) 3 y = 2 x + 3 (d) 4 x + 3 y = 9 (e) 5 x − 10 y −15 = 0 (f) 6 y − 3 x + 8 = 0 8 Find the mid-point of the line joining the points A (−5, 12) and B (1, 4). 9 The diameter of a circle is PQ , where P and Q are the points (−4, 3) and (4, 5) respectively. (a) The centre of the circle is the mid-point M of the diameter PQ . Find the coordinates of  M . (b) Show that the diameter of the circle PQ is 2  √ 17. 10 Find the lengths of the lines joining each of the following pairs of points: (a) (1, −2) and (6, 1) (b) (−4, 0) and (0, −3) (c) (0, 8) and (4, 7) 11 Points A and B are joined by a straight line. If the coordinates of A are (2, 3) and the mid-point of the line is at (4, 4), find the coordinates of point  B . 12 The points A and B have coordinates (0, 2) and (5, k ) respectively. If the gradient of the line joining points A and B is 4 5 , find the value of k . 13 Find the gradients of each of the following lines: (a) y = 4 x − 1 (b) 2 y = 3 x + 6 (c) 4 y − x = 6 (d) 3 y − 2 x − 9 = 0 14 The equation of line AB is 5 x − 2 y = 2. A is the point (4, 9) and B is the point (2, k ). (a) Show that k = 4. (b) Find the coordinates of the mid-point of AB . 2 Coordinate geometry 128