CO-ORDINATE GEOMETRY

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35. y B C A O x The diagram, not drawn to scale, shows a trapezium OABC with OA parallel to CB. Given that B is the point (4, 3), C is the point (0, 2) and the diagonal CA is parallel to the xaxis, calculate the coordinates of A. {Hint: you do not need to find the equations of any lines etc.!} 36. The diagram shows a square OABC. A is the point (7, 1). y B Find, in any order, the coordinates of B and C. C A(7, 1) O x www.mathsguru.co.uk
Answers. 1. a) 5 units b) 17 units c) 74 units d) 4 units e) 10 units f) 10 units. 2. a) 6 units b) 106 units c) 53 units d) 137 units e) 202 units f) 125 units 3. a) (6, 1) b) (2, 45) c) (35, 2) d) (1, 05) e) (25, 7) f) (15, 15). 4. a) XY = 5 units, YZ = 5 units, XZ = 50 units. b) Isosceles & rightangled. c) M = (25, 15). d) 125 units 2 . 5. a) M = (7, 0), N = (4, 4). b) PR = 10 units, MN = 5 units etc. 7. a) All 4 sides are of length 173 units. b) both mid-points coincide at (35, 05). c) {PQRS is actually a rhombus!}. 8. a = ± 5 2 . 9. a) 3, 1. b) 4, 1. c) 2, 3. d) 3, 2. e) 3, 1. f) 4, 3. g) 2, 7. h) 3, 1. i) 3, 4. j) 1,4. k) 1, 2. l) 4, 1. m) 1.5, 3. n) 2.5, 1. o) 3 2 , 3. p) 1, 2. q) 2, 7. r) 3, 1. s) 1, 2. t) 3, 2. u) 1 2 , 2. v) 2, 0. w) 2, 3. x) 7 3 , 3. y) 1 2 , 35. z) 0, 7. 10. i) a) 2 b) 25 c) 35 d) 2 e) 3 f) 1 www.mathsguru.co.uk g) 1 h) j) 1 2 . 1 2 i) 11. QR and PS both have gradients of 1.5 and thus are parallel. 12. Both gradients = 43 . P, Q and R are collinear (lie on a straight line). 13. i) AB = 1, AC = 1. ii) DE = 2, DF = 1 . 2 iii) GH = 4, GI = 1 . 4 iv) JK = 5, JL = 1 . 5 v) MN = 3, MO = 1 . 3 vi) PQ = 1 2 , PR = 2. The product of the gradinets of perpendicular lines = 1 !!! 14. a) i) and iv). b) iii). c) iv). d) ii). e) i) and ii). f) iii). 15. a) 2, 2; parallel b) 2 7 1 2 , 2; perpendicular 1 c) 3 , 3; perpendicular d) 5,5; parallel. 16. a) 2, 1 2 , 3 respectively.
Page 1 and 2: COORDINATE GEOMETRY 1. Using the po
Page 3 and 4: i) Find, by calculation, the gradie
Page 5 and 6: 17. Show that the triangle formed b
Page 7: 28. The coordinates of A and B are

CO-ORDINATE GEOMETRY

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