y hsn.uk.net Straight Line Paper 1 Section A Each correct answer in this section is worth two marks.
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1 Straight Line Paper 1 Section Each correct answer in this section is worth two marks. 1. The line with equation = a + 4 is perpendicular to the line with equation = 0. What is the value of a?. 3 B D The line through the points ( 2, 5) and (7, a) has gradient 3. What is the value of a?. 8 B D What is the distance, in units, between the points ( 1, 2) and (4, 5)?. 8 B D The equation of a line is 3 = a + 1 where a = 0 is a constant. Given that the line has a gradient of 7 5, what is the value of a? B D What is the distance, in units, between the points (a, b) and ( b, a)?. 2 a 2 + b 2 B. 2(a + b) ( a ). 2 + b D. 2 a 2 + b 2 hsn.uk.net Page 1 6. The line with equation = 3 a + 4, where a = 0 is a constant, is perpendicular to the line with equation = What is the value of a?. 6 B D. 6 Questions marked c SQ
2 7. The line l passes through (3, 2) 10. Triangle B is shown below. and is parallel to the line with equation = What is the equation of l? B = 0 B. 2 7 = = 0 D. 2 5 = 0 D Here are two statements about the line BD: I. BD is an altitude of triangle B II. BD is the perpendicular bisector of 8. Find the equation of the line passing through (6, 4) and parallel to the line with equation = = 0 B = = 0 Which of the following is true?. neither statement is correct B. onl statement I is correct. onl statement II is correct D. both statements are correct D = 0 9. Given that (1, 0) is the midpoint of ( 3, a) and B(b, 2), what are the values of a and b? a b. 2 4 B D. 4 2 hsn.uk.net Page 2 Questions marked c SQ
3 11. Triangle B with vertices ( 4, 1), B(4, 3) and (1, 5) is shown below. B M Point M(0, 2) is the midpoint of B. What is the equation of the median through? = 0 B = = 0 D. 3 1 = Triangle B with vertices (6, 7), B(7, 0) and ( 1, 2) is shown below. B The line through and B has gradient 1 4. Find the equation of the altitude through = 0 B = = 0 D = 0 hsn.uk.net Page 3 Questions marked c SQ
4 [END F PPER 1 SETIN ] Paper 1 Section B 13. Three lines have equations = 0, 3 17 = 0 and 3 10 = 0. Determine whether or not these lines are concurrent The points and B have coordinates (a, a 2 ) and (2b, 4b 2 ) respectivel. Determine the gradient of B in its simplest form Find the equation of the straight line which is parallel to the line with equation = 5 and which passes through the point (2, 1) rag 17. The kite BD has( vertices) (1, 8), B(0, 2), ( 3, 4) and D 21 5, k as shown in the (1, 8) diagram. (a) Determine the value of k. 5 (b) Find the area of triangle BD. 4 ( ) D 21 5, k ( 3, 4) B(0, 2) hsn.uk.net Page 4 Questions marked c SQ
5 18. (a) The line l 1 passes through the point (1, 10) and is perpendicular to the line with equation + 2 = 1. Find the equation of l 1. 3 (b) The line l 2 passes through the point (6, 5) and makes an angle a with the positive direction of the -ais, where tan a = 1 3. Find the equation of l 2. 2 (c) Determine the coordinates of the point of intersection of l 1 and l Triangle B has vertices (1, 2), B(8, 2) and (4, 6). D (a) Find the equation of the line through the collinear points, and D. (4, 6) 2 (b) Triangle BD is right-angled at B. Find the equation of BD. 1 (c) Find the coordinates of D. (1, 2) B(8, 2) The equation of a straight line is 3 + a + 1 = 0, where a = 0 is a constant. Given that this line has a gradient of 1 3, find the value of a, and hence state the coordinates of the point where the line cuts the -ais The line is the diameter of a circle with B ling on the circumference as shown below. ( 1, 5) B(3, 7) is the point ( 1, 5) and B(3, 7). Find the equation of the chord B. 3 hsn.uk.net Page 5 Questions marked c SQ
6 22. The diagram below shows the right-angled triangle PQ and a circle with centre (0, 5) and diameter S. S R Q 3 6 P Find the equation of the chord RS Triangle B has vertices ( 3, 5), B(9, 9) and (9, 3). (a) Write down the equation of B. 1 (b) Find the equation of the altitude from. 2 (c) Find the equation of the perpendicular bisector of B. 4 (d) Find where the perpendicular bisector of B and the altitude from intersect. 2 B 24. Triangle B is shown in the diagram below. ( B 2 ) 3, 7 and lie on the -ais, and B is the point ( 2 ) 3, 7. (a) The line B has a gradient of 1 2. Find the equation of B. 2 (b) B is part of the line with equation = 0. Find the length of. 2 Questions marked c SQ hsn.uk.net Page 6
7 25. The line with equation 3 + a + 1 = 0, where a is a constant, is perpendicular to the line with equation 2 = 2. Find the value of a Triangle B has vertices (4, 7), B( 2, 1) and (6, 3). (a) Find the equation of line p, the PSfrag median from. 3 (b) Find the equation of line q, the altitude B from. 3 (c) Find the point of intersection of the lines p and q The line with equation = 0 intersects the -ais at P and the -ais at R. (a) Write down the coordinates of P and R. 1 (b) The perpendicular bisector of PR meets the line = 1 at Q. Find the coordinates of Q. 5 (c) Show that P, Q and R could be three vertices of a square Triangle PQR is shown in the diagram. P(1, 3) R Q(7, 2) The line PR has equation = 0, and QR has equation 5 17 = 0. (a) Find the coordinates of point R. 2 (b) Hence find the equation of the median through R. 3 hsn.uk.net Page 7 Questions marked c SQ
8 29. The points (3, 2), B(2a, 12) and (a, 1) are collinear. Find the value of the constant a Triangle B is shown in the diagram. ( 4, 6) B(4, 3) The line has equation = 20, and B has equation + 6 = 14. Find the equation of the altitude through. 5 [END F PPER 1 SETIN B] hsn.uk.net Page 8 Questions marked c SQ
9 Paper 2 1. Find the equation of the perpendicular bisector of the line joining (2, 1) and B(8, 3) rag 3. rag 4. rag hsn.uk.net Page 9 Questions marked c SQ
10 5. rag 6. rag 7. rag 8. Find the equation of the line through the point (3, 5) which is parallel to the line with equation = rag hsn.uk.net Page 10 Questions marked c SQ
11 10. The vertices of a triangle are P( 1, 1), Q(2, 1) and R( 6, 2). Find the equation of the altitude of triangle PQR, drawn from P Find the equation of the median D of triangle B where the coordinates of, B and are ( 2, 3), ( 3, 4) and (5, 2) respectivel rag 13. rag 14. Triangle B has vertices ( 1, 6), B( 3, 2) and (5, 2). ( 1, 6) Find (a) the equation of the line PSfrag p, the median from of triangle B. (5, 2) 3 (b) the equation of the line q, the perpendicular bisector of B. 4 (c) the coordinates of the point of B( 3, 2) intersection of the lines p and q. 1 Questions marked c SQ hsn.uk.net Page 11
12 15. rag 16. rag 17. rag hsn.uk.net Page 12 Questions marked c SQ
13 18. P, Q and R have coordinates (1, 2), (6, 3) and (9, 14) respectivel and are three vertices of a kite PQRS. (a) Find the equations of the diagonals of this kite and the coordinates of the point where the intersect. 7 (b) Find the coordinates of the fourth verte S Points (2, 3) and (8, 11) are the end points of a diagonal of rectangle BD. The diagonal BD is parallel to the -ais. Find the area of the rectangle The diagram shows a rhombus BD. The points B and D have coordinates (3, 5) and (9, 3) respectivel. The equation of D is = 6. B Find the size of angle D. 6 D 21. The diagram shows triangle B. circle passes through all the vertices of the triangle. is a diameter of the circle. The equation of B is 3 = 2. (a) Find the gradient of B. 3 (b) B makes an angle of a radians with the positive direction of the -ais. Find the value of a. 2 B a hsn.uk.net Page 13 Questions marked c SQ
14 22. The line l passes through points ( 2, 6) and B(5, 1), as shown below. ( 2, 6) P B(5, 1) The line through and P is perpendicular to l, and lies on the -ais. (a) Find the equation of the line through and P. 3 (b) Hence find the coordinates of P. 3 (c) alculate the area of the triangle P Find the equation of the straight line passing through the point ( 2 ) 3, 7, with a gradient of The line with equation = 0 makes an angle of φ with the -ais as shown below = 0 φ alculate the value of φ correct to two decimal places. 4 hsn.uk.net Page 14 Questions marked c SQ
15 25. The points R(1, 2), S(5, 8) and T(11, 4) lie on the circumference of a circle. S = 0 R T The line with equation = 0 is the perpendicular bisector of ST. (a) Find the equation of the perpendicular bisector of RS. 4 (b) The centre of the circle is the point where the perpendicular bisectors of RS and ST intersect. alculate the coordinates of the centre of the circle Triangle PQR has vertices P(1, 4), Q(6, 14) and Q(6, 14) R(7, 6). (a) Find the equation of the median QS. 3 (b) Find the equation of the altitude RT. 3 (c) The median QS and the altitude RT intersect at T. R(7, 6) Find the coordinates of. S 3 P(1, 4) 27. The vertices of the triangle PQR are P(2, 6), Q( 4, 4) and R( 3, 7). (a) Find the equation of the median through R. 3 (b) Find the equation of the altitude through Q. 3 (c) The median through R and the altitude through Q intersect at point T. alculate the coordinates of T. 3 [END F PPER 2] hsn.uk.net Page 15 Questions marked c SQ
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