CHAPTER 5 : THE STRAIGHT LINE
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1 EXERCISE 1 CHAPTER 5 : THE STRAIGHT LINE 1. In the diagram, PQ is a straight line. P Find (a) the -intercept, (b) the gradient, of the straight line. Q (5,18) Q Answer :a).. b) 3 P 0 Find a) the gradient of PQ b) the equation of straight line PQ Answer :a) b) 3. Determine the gradient of the straight line = F Answer : E(-2,6) 0 G 5. The Determine diagram shows the -intercept two straight of the lines, straight EF and line FG, 2 on a = Cartesian - plane. The gradient of EF is 1 and the distance of FG is 10 units. The -intercept of FG is 38 Answer :.
2 6. The gradient of the straight line = 13 Answer : The - intercept of the straight line 4 2 = 12 is 8. In the diagram, AB is a straight line. Answer : A B What is the gradient of AB? 9. In the diagram, R = S. The equation of RS is Answer :.. S R In the diagram, MLT is a right-angled triangle.. L(6,7) Answer: M T(6,4) 0 Find a) the coordinate of M, b) the equation of the straight line LT. Answer :.a)... b). 39
3 EXERCISE 2 CHAPTER 5 : THE STRAIGHT LINE 1. P Q (3,5) R The diagram shows a parallelogram PQR. Given that the gradient of P = The -intercept of line QR is... Answer : 2. Q(0,5) R(12,3) P 0 S(4,k) In the diagram, PQRS is a parallelogram. The equation of the straight line RS is 2 = 6. Find a) the value of k, b) the gradient of the straight line QR, Answer: a) b). 40
4 3. In the diagram, PQR is a parallelogram and is the origin. Find a) the gradient of the straight line R, b) the equation of the straight line PQ Q R(2,4) P(6,1) 0 Answer: a) b). 4. In the diagram PQRS is a parallelogram P(-2,12) Q S 0 a) Given that the gradient of line PQ is -3, find the equation of PQ b) Find the coordinate of point R. R Answer a)... b)... 41
5 5. In the diagram, LH is a straight line. Given that the gradient of the straight line LH is -1. L(-3,9) H(0,k) Find (a) the value of k, (b) the equation of the stragiht line LH. 0 Answer: a) b). 6. In the diagram above, ABCD is a parallelogram and is the origin. The straight line BD is parallel with the -ais and the equation of line AB is = B(6,10) A C Find (a) the -intercept of the straight line AB, (b) the gradient of AD, 0 D Answer: a) b) 42
6 Q(4,8) S(10,2) 0 P(2,0) R 7. In the diagram, PQ is parallel to RS and is the origin. Find a) the gradient of RS b) the - intercept of RS Answer: a) b) 8. In the diagram M = 3 1 A and the length of the straight line A is 9 units. A B 0 M (a) Find the coordinate of point B. (b) Calculate the gradient of line MB. Answer a)... b)... 43
7 9. In the diagram, CD is parallel to EF. D = 3+5 F 0 C Find (a) the -intercept of line CD, (b) the equation of straight line EF. E(-1,-4) Answer: a) b) 10. In the diagram, EFGH is a parallelogram. Given that the gradient of line EF is 2 5. Find the coordinate of point G. E H(8,5). F 0 G Answer: 44
8 DIAGNSTIC TEST CHAPTER 5 : THE STRAIGHT LINE 1. In Diagram 1, MN is a straight line. M N Diagram 1 Find the gradient of MN. A -2 3 B 4 3 C - 4 D 2 2. Given that the equation of a straight line is = 0. Find the -intercept of the straight line. A -1 B -2 C -3 D In Diagram 2, the length of C is 2 units. B A(10,6) C Diagram 2 The gradient of line BC is A 3 B 4 C -4 45
9 D -3 P(8,2) R(-2,-8) Diagram 3 4. Based on Diagram 3, find the equation of line PR. A = - 6 B = C = + 6 D = 6 5. In Diagram 4, the equation of the line WZ is = 4 3. Q (8, k) is a point on the line WZ. W Q (8, k) Diagram 4 Z 0 Find the value of k. A 6 B 7 C 8 D 9 6. The equation of a straight line passing through the point ( -3, 8 ) and parallel to the line = is A = B 3 = C 3 = D =
10 E Diagram 5 0 G 7. In Diagram 5, E = G. Find the gradient of line EG. A 1 B -1 C 2 D -2 U(-3,6) Diagram In Diagram 6, find the gradient of the line U. A 1 B -1 C 2 D The -intercept of the straight line 4 = 3 2 is 3 A 4 1 B - 2 C D
11 R J ( 4, 8 ) Diagram 7 0 P 10. In Diagram 7, the length of P is 10 units. The equation of line PR is 4 A = B = C = D =
12 CHAPTER 5 : THE STRAIGHT LINE EXERCISE 1 1. R(5,7) Q(1,4) P(-1,0) S Diagram 1 In Diagram 1, straight lines PQ and RS are parallel. Find the a) gradient of the line PQ, b) equation of the line RS, c) -intercept of the line RS. 2.. N K M(5,0) L Diagram 2 In Diagram 2, straight lines KL and MN are parallel. The equation of the line KL is = 0. Find the a) gradient of the line KL, b) equation of the line MN, c) -intercept of the line MN. 49
13 3. F(3,k) G(7,10) E H Diagram 3 In Diagram 3, straight line FG is parallel to the -ais while the lines EF and GH are parallel. The gradient of the line EF is 2. a) State the value of k, b) Find the equation of the line GH, c) Find the coordinates of the point E. 4. M (5,20) L K Diagram 4 In Diagram 4, KLM is a parallelogram and line ML is parallel to the -ais.point L is on the -ais. a) State the coordinates of the point L, b) Find the -intercept of the line KL, c) Find the equation of the line KL. 50
14 5. V(8, k) U T(-2,1) S W Diagram 5 In Diagram 5, the equation of the straight line STUV is 2 = + 4. The lines T and UW are parallel. Find the a) value of k, b) -intercept of the line STUV, c) equation of the line UW. 51
15 EXERCISE 2 1. CHAPTER 5 : THE STRAIGHT LINE B(-3,10) C A Diagram 1 The equation of the straight line AB in Diagram 1 is = a) State the equation of the straight line BC, b) Find the -intercept of the straight line AB, c) Find the equation of AC. U Y Z (6,5) C (-2,3) V D (8,-2) 2. Diagram 2 In Diagram 2, the straight line UV is parallel to CD. is the origin. a) Calculate the gradient of line CD, b) Find the equation of line UZV, c) Find - intercept of line UZV. 52
16 3. Q (h, 3 ) R P( -8, 0 ) 0 S ( 6, 0 ) Diagram 3 In Diagram 3, the gradient of the straight line PQR is 3.Find the a) value of h b) -intercept of the line RS c) equation of the line RS 4. B (2, 8 ) C A (2, 3 ) 0 Diagram 4 In Diagram 4, ABC is a parallelogram. Find the a) coordinates of C b) equation of the straight line BC 53
17 5. Y Q S 12 P -4 3 X R Diagram 5 In Diagram 5, straight lines PQ and RS are parallel. a) State the gradient of PQ b) Find the equation of RS c) Find the intercept of RS 54
18 CHAPTER 5 : THE STRAIGHT LINE DIAGNSTIC TEST 1. A B (6, 5) D C (6, 0) Diagram 1 In Diagram 1, A and D are located on the -ais and ABCD is a parallelogram. If the gradient of AB = - 2 1, a) State the gradient of CD. b) Determine the coordinates of D. c) Find the equation of the straight line AB. [ 5 marks ] 2. P (0, 9) Q (5, 7) R (0, -5) Diagram 2 Diagram 2 shows a triangle PQR. a) State the -intercept of the straight line PQ, b) Find the equation of the straight line QR, c) Find the equation of a straight line that passes through P and parallel to the straight line QR. [ 5 marks ] 55
19 3. M P Diagram 3 N In Diagram 3, MN = 12 units and parallel to the -ais. Given N = 6 units and P = 3 2 MN, 4. a) State the coordinates of P, b) Find the gradient of the straight line PM, c) Find the equation of the straight line PM. A D = 2 + k [ 5 marks ] C E B Diagram 4 In Diagram 4, two straight lines AB and CD intersect at point (-1, 3). Given the gradient of AB is -1, find the a) value of k, b) equation of the straight line AB, c) coordinates of point E. [ 5 marks] 56
20 5. P (-3, 6) Q (h, k) M (4, 3) Diagram 5 R In Diagram 5, Q and PR intersect at M which is midpoint of Q. Given is the origin. Find a) the value of h and k, b) the equation of the straight line PR. [ 5 marks] 57
b UVW is a right-angled triangle, therefore VW is the diameter of the circle. Centre of circle = Midpoint of VW = (8 2) + ( 2 6) = 100
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