(13-18) 3B-Ch.8-Coordinate Geometry of Straight Lines - CQ

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Ch 8 Coordinate Geometry GHS Past Paper Question Bank – Conventional Question Page 1 of 5 Form 3 GHS Past Paper Question Bank – Conventional Question Coordinate Geometry Conventional Questions 1. [13-14 St Test 2, 3] In Figure 3 , L 1 L 2 at A (6, 24). B (18, 4) is a point on L 2 and L 1 cuts the x -axis at C . (a) Find the coordinates of C . (3 marks) (b) Find the area of ABC . (3 marks) (c) If point D lies on BC such that its x -coordinate is 3, find CD : DB . (2 marks) 2. [13-14 St Test 2, 6] In Figure 6 , ABCD is a rhombus with vertices A (0, a ), B ( b , 0), C (0, a ) and D ( b , 0). M is the mid-point of BC and AM = DM . (a) Find the coordinates of M . (1 mark) (b) Prove that ABCD is a square by the analytic approach. (3 marks) 3.[13-14 Final Exam, 5] In Figure 3 , CD is the perpendicular bisector of AB . CD cuts AB at point D . (a) Find the coordinates of D . (1 mark) (b) If the y -coordinate of point C is 7, find the x -coordinate of C . (2 marks) 4. [13-14 Final Exam, 10] In Figure 5 , ABCD is a parallelogram. E , F , G , and H are the mid-points of AB , BC , CD and DA respectively. (a) Find the value of k . (2 marks) (b) Prove that EFGH is a parallelogram by the analytical approach. (3 marks) (c) Prove that HF GF and hence find the area of FGH . (3 marks) Figure 3 O L 2 C A (6, 24) x y L 1 B (18, 4) O x y Figure 6 M C (0, a ) D ( b , 0) B ( b , 0) A (0, a ) D B (6 , 0) A (– 4 , 4) Figure 3 C y O x A (2, 3) B (10, 1) C (16, 9) D ( k , 7) E Figure 5 H G F
Ch 8 Coordinate Geometry GHS Past Paper Question Bank – Conventional Question Page 2 of 5 Form 3 GHS Past Paper Question Bank – Conventional Question 5. [14-15 Standardized Test, 1] It is given that P (–1, 6), Q (–3, 0) and R (1, 2). Prove that PQR is an isosceles right-angled triangle. (3 marks) 6. [14-15 Standardized Test, 7] In Figure 3 , L 1 // L 2 . L 1 passes through (–1, 0) and (0, –3). L 2 passes through A (1, 2) and cuts y -axis at B . (a) Find the coordinates of B . (2 marks) (b) If C ( c , d ) is a point on L 2 such that BC : BA = 5 : 2, find the coordinates of C . (2 marks) 7. [14-15 Final Exam, 9] A (–3, 4), B (9, 10) and C (0, 13) are the vertices of a triangle as shown in Figure 4 . (a) Prove that ABC is an isosceles right-angled triangle. (3 marks) (b) A line L (not shown in the figure) passes through point C and parallel to AB , (i) find the slope of L . (1 mark) (ii) Let D ( x , y ) be a point on L such that AB DA . Find the coordinates of D . (3 marks) 8. [14-15 Final Exam, 11] If C (4, 2) is a point on AB, and the coordinates of A and B are (2, –6) and (7, y ) respectively, find (a) AC : CB , (2marks) (b) the value of y . (1 mark) x y L 2 Figure 3 A (1, 2) B 0 –1 –3 C ( c , d ) L 1 x y C (0, 13) B (9, 10) A ( 3, 4) Figure 4
Ch 8 Coordinate Geometry GHS Past Paper Question Bank – Conventional Question Page 3 of 5 Form 3 GHS Past Paper Question Bank – Conventional Question 9. [15-16 Standardized Test, 6] In Figure 4 , A (–6, 0), B (–1, 6) and C (6, 0) are the vertices of ABC on the rectangular coordinate plane. BD is the height of ABC . (a) It is given that a a E 6 , 5 6 is a point on AB such that ED // BC , find the value of a . (2 marks) (b) It is given that F is a point on BC such that DF BC . By considering the area of BCD , find DF . (Leave your answer in surd form.) (3 marks) (c) BA is produced to a point G such that GA : GB = 1 : 3. Write down the coordinates of G . (1 mark) (d) A point H lies on BD such that BH : HD = 151 : 149. Gary claims that E , H and F are collinear. Do you agree? Explain briefly. (2 marks) 10. [15-16 Final Exam, 8] The coordinates of A and B are (–1, 2) and ( b , 8) respectively. It is given that C (2, 4) is a point on AB such that 2 : 1 : CB AC . (a) Find b . (2 marks) (b) If AB DB and the coordinates of D are (2 d , d ), find d . (2 marks) 11. [15-16 Final Exam, 17] In Figure 9 , the diagonals AC and BD of quadrilateral ABCD intersect at E . It is given that E is the mid-point of AC . (a) Write down the coordinates of E . (1 mark) (b) Find ABD by analytical approach. (3 marks) y B A D O C Figure 4 y B (10,10) A (6, 8) E D (2, 2) C (8, 6) O x Figure 9
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Ch 8 Coordinate Geometry GHS Past Paper Question Bank – Conventional Question Page 4 of 5 Form 3 GHS Past Paper Question Bank – Conventional Question 12. [16-17 Standardized Test, 6] Consider the points A (–6, 0), B (2, 0) and C (4, –5). AC cuts the y -axis at M (0, y ). (a) Show that AM : MC = 3 : 2. (2 marks) (b) Hence, find the area of BCM. (4 marks) 13. [16-17 Final Exam, 13] In Figure 3 , A ( 3.5, 2), B (3, 0) and C (2, 6) are three points on the rectangular coordinate plane. (a) Find the length of AB . (2 marks) (b) If D is the mid-point of BC , determine whether AD is perpendicular to BC ? Explain your answer. (2 marks) (c) E is a point on AB such that 2 : 3 : EB AE . Jason claims that AC ED // . Do you agree? Explain your answer. (2 marks) 14. [17-18 Standardized Test, 4] A (8, 12), B (4, 2) and C ( c , 0) are the vertices of a triangle. The mid-point K of AC lies on the y -axis. (a) (i) Find the value of c . (2 marks) (ii) Write down the coordinates of K . (1 mark) (b) D is a point such that ABCD is a quadrilateral with AK : AC = BK : BD , where B , K and D are collinear. Kitty claims that ABCD must be a parallelogram. Do you agree? Explain briefly. (2 marks) 15. [17-18 Standardized Test, 5] A (15, –5), B ( b , –1) and O (0, 0) are the vertices of AOB . A straight line L which passes through P (1, 2 3 ) and Q ( 2 , –3) is parallel to BO . (a) Find the inclination of PQ . ( 3 marks) (b) Find the value of b. (1 mark) (c) Show that AOB is a right-angled triangle . (2 marks) 16. [17-18 Final Exam, 11] In Figure 4 , the coordinates of the points A and B are (6, 2) and (2, 2) respectively. A' is the reflection image of A with respective to the x -axis. (a) Write down the coordinates of A' . (1 mark) (b) Prove that BA' is perpendicular to OB . (2 marks) y A ( 3.5, 2) Figure 3 x C (2, 6) O B (3, 0) y B (2, 2) O A (6, 2) x x Figure 4
Ch 8 Coordinate Geometry GHS Past Paper Question Bank – Conventional Question Page 5 of 5 Form 3 GHS Past Paper Question Bank – Conventional Question 17. [17-18 Final Exam, 17] In Figure 8 , A (5, 2), B (5, 6) and C are the vertices of a triangle. It is given that D (4, 1) is the mid-point of AC and the coordinates of E are (5, 2). BD and CE intersect at G . (a) Find the coordinates of C . (b) (i) Show that CG : GE = 2 : 1. (ii) Find the coordinates of G . (c) It is given that P is the circumcentre of ABC . Find the coordinates of P . x y A (5, 2) O D (4, 1) B (5, 6) C G E (5, 2) Figure 8