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# F4 05 The Straight Line

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### F4 05 The Straight Line

1. 1. ppr maths nbk CHAPTER 5 : THE STRAIGHT LINE EXERCISE 1 1. In the diagram , PQ is a straight line. P y 4 2 – 4 – 3 – 2 – 1 0 1 2 x – 2 Q Find (a) the y-intercept, (b) the gradient , of the straight line. Answer :a)…………………….…. b)……………………… 2. y Q (5,18) 3 P 0 x Find a) the gradient of PQ b) the equation of straight line PQ Answer :a)……………………… b)……………………… x 3. Determine the gradient of the straight line y = − +9 4 Answer :………………… 4. y F E(-2,6) 0 G 5. Determine shows two straight lines, EF and FG, – x a= - The diagram the y-intercept of the straight line 2y on Cartesian plane. The gradient of EF is 1 and the distance of FG is 10 units. The x-intercept of FG is 38 Answer :………………………….
2. 2. ppr maths nbk 6. The gradient of the straight line 2x + 6y = 13 Answer :………………………... 7. The x - intercept of the straight line 4x – 2y = 12 is Answer :……………………… 8. In the diagram, AB is a straight line. y A -12 0 x -3 B What is the gradient of AB ? Answer :……………………….. 9. In the diagram, OR = OS. The equation of RS is y S R x -4 0 Answer:………………………… 10. In the diagram , MLT is a right-angled triangle. . y L(6,7) M T(6,4) 0 x Find a) the coordinate of M, b) the equation of the straight line LT. Answer :.a)…............................. b)……………………. 39
3. 3. ppr maths nbk CHAPTER 5 : THE STRAIGHT LINE EXERCISE 2 1. y P Q (3,5) O R x 5 The diagram shows a parallelogram OPQR. Given that the gradient of OP = - . 3 The x-intercept of line QR is …...... Answer :……………………… 2. y Q(0,5) R(12,3) P 0 x S(4,k) In the diagram, PQRS is a parallelogram. The equation of the straight line RS is 2y = x – 6. Find a) the value of k, b) the gradient of the straight line QR, Answer: a)…………………… b)…………………. 40
4. 4. ppr maths nbk 3. In the diagram, OPQR is a parallelogram and O is the origin. Find a) the gradient of the straight line OR, b) the equation of the straight line PQ y Q R(2,4) P(6,1) 0 x Answer: a)………………… b)…………………. 4. In the diagram PQRS is a parallelogram P(-2,12) y Q S 0 x R a) Given that the gradient of line PQ is -3, find the equation of PQ b) Find the coordinate of point R. Answer a)................................. b) ................................ 41
5. 5. ppr maths nbk 5. In the diagram, LH is a straight line. Given that the gradient of the straight line LH is -1. y L(-3,9) H(0,k) 0 x Find (a) the value of k, (b) the equation of the stragiht line LH. Answer: a)…………………… b)……………………. 6. In the diagram above, ABCD is a parallelogram and O is the origin. The straight 2 line BD is parallel with the y-axis and the equation of line AB is y = x + 4. 3 y B(6,10) A C 0 D x Find (a) the x-intercept of the straight line AB, (b) the gradient of AD, Answer: a)…………………… b)…………………… 42
6. 6. ppr maths nbk y Q(4,8) S(10,2) 0 P(2,0) R x 7. In the diagram, PQ is parallel to RS and O is the origin. Find a) the gradient of RS b) the x- intercept of RS Answer: a)…………………… b)…………………… 1 8. In the diagram OM = OA and the length of the straight line OA is 9 units. 3 y A B 0 M x (a) Find the coordinate of point B. (b) Calculate the gradient of line MB. Answer a).................................. b).................................. 43
7. 7. ppr maths nbk 9. In the diagram, CD is parallel to EF. y D y = 3x+5 F 0 x C Find E(-1,-4) (a) the x-intercept of line CD, (b) the equation of straight line EF. Answer: a)…………………… b)…………………… 5 10. In the diagram, EFGH is a parallelogram. Given that the gradient of line EF is . Find 2 the coordinate of point G. y E H(8,5) . F 0 G x Answer: …………………… 44
8. 8. ppr maths nbk CHAPTER 5 : THE STRAIGHT LINE DIAGNOSTIC TEST 1. In Diagram 1, MN is a straight line. M y 6 x 0 8 Diagram 1 N 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 x – 2y + 3 = 0. Find the x-intercept of the straight line. A -1 B -2 C -3 D -4 3. In Diagram 2, the length of OC is 2 units. y ⋅ B ⋅ A(10,6) Diagram 2 O ⋅C x The gradient of line BC is A 3 B 4 C -4 45
9. 9. ppr maths nbk D -3 y ⋅ P(8,2) O x ⋅ R(-2,-8) Diagram 3 4. Based on Diagram 3, find the equation of line PR. A y = -x – 6 B y = -x + 6 C y=x+6 D y=x–6 3 5. In Diagram 4, the equation of the line WZ is y = x. 4 Q (8, k) is a point on the line WZ. y ⋅ Q (8, k) W Diagram 4 0 x Z 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 2 the line y = x + 5 is 3 2 A y= x+8 3 B 3y = 2x + 10 C 3y = 2x + 30 2 D y = x -3 3 46
10. 10. ppr maths nbk y E Diagram 5 0 G x 7. In Diagram 5, OE = OG. Find the gradient of line EG. A 1 B -1 C 2 D -2 y ⋅U(-3,6) Diagram 6 x 0 8. In Diagram 6, find the gradient of the line OU. A 1 B -1 C 2 D -2 9. The y-intercept of the straight line 4y = 3 – 2x is 3 A 4 1 B - 2 3 C - 4 1 D 2 47
11. 11. ppr maths nbk y R ⋅ ⋅J ( 4, 8 ) Diagram 7 0 ⋅ P x 10. In Diagram 7, the length of OP is 10 units. The equation of line PR is 4 A y= x+8 5 4 B y=- x+8 5 5 C y = x +4 4 5 D y=- x+4 4 48
12. 12. ppr maths nbk CHAPTER 5 : THE STRAIGHT LINE EXERCISE 1 1. y R(5,7) Q(1,4) x P(-1,0) O 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) x-intercept of the line RS. 2. y. N K x O M(5,0) L Diagram 2 In Diagram 2, straight lines KL and MN are parallel. The equation of the line KL is y + 3x + 3 = 0. Find the a) gradient of the line KL , b) equation of the line MN , c) y-intercept of the line MN. 49
13. 13. ppr maths nbk 3. y F(3,k) G(7,10) E O H x Diagram 3 In Diagram 3, straight line FG is parallel to the x-axis 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. y M (5,20) L O x K Diagram 4 In Diagram 4, OKLM is a parallelogram and line ML is parallel to the y-axis.Point L is on the x-axis. a) State the coordinates of the point L , b) Find the y-intercept of the line KL, c) Find the equation of the line KL. 50
14. 14. ppr maths nbk 5. y V(8, k) U T(-2,1) x S O W Diagram 5 In Diagram 5 , the equation of the straight line STUV is 2y = x + 4. The lines OT and UW are parallel. Find the a) value of k , b) y-intercept of the line STUV , c) equation of the line UW . 51
15. 15. ppr maths nbk CHAPTER 5 : THE STRAIGHT LINE EXERCISE 2 1. y B(-3,10) C x A O Diagram 1 The equation of the straight line AB in Diagram 1 is y = 2 x + 16. a) State the equation of the straight line BC, b) Find the x-intercept of the straight line AB, c) Find the equation of AC. Y U Z (6,5) C (-2,3) V O D (8,-2) 2. Diagram 2 In Diagram 2, the straight line UV is parallel to CD. O is the origin. a) Calculate the gradient of line CD, b) Find the equation of line UZV, c) Find x- intercept of line UZV. 52
16. 16. ppr maths nbk 3. y R Q (h , 3 ) x 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) y-intercept of the line RS c) equation of the line RS 4. y B (2 , 8 ) C A (2 , 3 ) x 0 Diagram 4 In Diagram 4, OABC is a parallelogram. Find the a) coordinates of C b) equation of the straight line BC 53
17. 17. ppr maths nbk 5. Y Q S 12 -4 3 X P 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. 18. ppr maths nbk CHAPTER 5 : THE STRAIGHT LINE DIAGNOSTIC TEST y 1. A B (6, 5) D x O C (6, 0) Diagram 1 In Diagram 1, A and D are located on the y-axis and ABCD is a parallelogram. 1 If the gradient of AB = - , 2 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) O x R (0, -5) Diagram 2 Diagram 2 shows a triangle PQR. a) State the y-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. 19. ppr maths nbk y 3. M P x O N Diagram 3 In Diagram 3, MN = 12 units and parallel to the y-axis. Given NO = 6 units and 2 PO = MN, 3 a) State the coordinates of P, b) Find the gradient of the straight line PM, c) Find the equation of the straight line PM. [ 5 marks ] y 4. D y = 2x + k A x O E B C 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. 20. ppr maths nbk 5. y P (-3, 6) Q (h, k) M (4, 3) x O R Diagram 5 In Diagram 5, OQ and PR intersect at M which is midpoint of OQ. Given O is the origin. Find a) the value of h and k, b) the equation of the straight line PR . [ 5 marks] 57