CO-ORDINATE GEOMETRY

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24. a) Find the equation of the line which passes through the points (2, 2) and (5, 8). b) Does the line pass through the point ( 2, 6 ) ? Give a reason for your answer. 25. a) Find the gradient of the line joining the points A ( 1, 2) and B(3, 4). b) Hence find the equation of the line joining the points A and B in the form y = mx + c. c) Rearrange the formula to show that the equation of the line can be written 2y x = 5. d) The line cuts the x-axis at the point P and the y-axis at the point Q. Find the co-ordinates of P and Q. y 2y x = 5 Q P x 26. a) Find the gradient of the line joining the points A ( 1, 3) and B(4, 1). b) Hence find the equation of the line joining the points A and B in the form y = mx + c. c) Rearrange the formula to show that the equation of the line can be written 3y + 2x = 11. d) The line cuts the x-axis at the point P and the y-axis at the point Q. y Find the co-ordinates of P and Q. 3y + 2x =11 Q 27. Points A and B have co-ordinates (3, 1) and (7, 4). P x a) Find the co-ordinates of M, the midpoint of AB. b) Find the gradient of AB. c) Find the equation of the perpendicular bisector of AB. d) Find the co-ordinates of the point where this line crosses the x-axis. www.mathsguru.co.uk A M B
28. The coordinates of A and B are (3, 2) and (4, 5) respectively. Find the coordinates of the midpoint of AB and the gradient of AB. Hence find the equation of the perpendicular bisector of AB, giving your answer in the form ax + by + c = 0, where a, b and c are integers. 29. The coordinates of A and B are (3, 3) and (6, 0) respectively. Find the coordinates of the midpoint of AB and the gradient of AB. Hence find the equation of the perpendicular bisector of AB, giving your answer in the form ax + by + c = 0, where a, b and c are integers. 30. The equation of the straight line l 1 is x + 3y 33 = 0. The point P is (3, 0) and the point Q is (6, 9). The straight line l 2 is parallel to l 1 and passes through P. i) Find the equation of l 2 , giving your answer in the form ax + by + c = 0. ii) Verify that Q lies on l 1 . iii) Show that the line joining P and Q is perpendicular to l 1 . iv) Find the perpendicular distance between l 1 and l 2 . 31. The equation of the straight line l 1 is x + 6y 24 = 0. The point P is (1, 64) and the point Q is (12, 2). The straight line l 2 is parallel to l 1 and passes through P. i) Find the equation of l 2 , giving your answer in the form ax + by + c = 0. ii) Verify that Q lies on l 1 . iii) Show that the line joining P and Q is perpendicular to l 1 . iv) Find the perpendicular distance between l 1 and l 2 . 32. The straight line p passes through the point (10, 1) and is perpendicular to the line r with equation 2x + y = 1. Find the equation of p. Find also the coordinates of the point of intersection of p and r, and deduce the perpendicular distance from the point (10, 1) to the line r. 33. The quadrilateral ABCD has vertices A(2, 5), B(0, 9), C(5, 6) and D(3, 6). a) Find the equations of the diagonals AC and BD. b) Find the coordinates of the point, P, where these two diagonals meet. {Hint: simultaneous equations!} c) Show that P is not the midpoint of either of the two diagonals. 34. a) Find the equation of the perpendicular from the point A(5, 3) to the line 2x y + 4 = 0. b) Find the co-ordinates of the point P where the two lines meet. 2x y + 4 = 0 c) Hence find the shortest distance from A to the line 2x y + 4 = 0. P www.mathsguru.co.uk A
Page 1 and 2: COORDINATE GEOMETRY 1. Using the po
Page 3 and 4: i) Find, by calculation, the gradie
Page 5: 17. Show that the triangle formed b
Page 9 and 10: Answers. 1. a) 5 units b) 17 units

CO-ORDINATE GEOMETRY

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