Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 963 · 40 questions

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

1. 1.In which quadrant does the point (8, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
2. 2.In which quadrant does the point (−9, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
3. 3.In which quadrant does the point (8, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
4. 4.In which quadrant does the point (2, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
5. 5.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
6. 6.What is the midpoint of the line joining (4, 5) and (16, 1)? (a) (6, 2) (b) (20, 6) (c) (3, 10) (d) (10, 3)
7. 7.What is the midpoint of the line joining (2, 3) and (14, 15)? (a) (9, 8) (b) (16, 18) (c) (8, 9) (d) (6, 6)
8. 8.In which quadrant does the point (−2, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
9. 9.In which quadrant does the point (−6, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
11. 11.What is the midpoint of the line joining (5, 11) and (11, 9)? (a) (16, 20) (b) (3, 1) (c) (10, 8) (d) (8, 10)
12. 12.What is the midpoint of the line joining (2, 1) and (12, 5)? (a) (3, 7) (b) (7, 3) (c) (14, 6) (d) (5, 2)
13. 13.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
14. 14.In which quadrant does the point (1, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
15. 15.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
16. 16.What is the distance between the points (1, 0) and (13, 16)? (a) 400 (b) 21 (c) 28 (d) 20
17. 17.In which quadrant does the point (−2, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
18. 18.What is the distance between the points (8, 9) and (14, 1)? (a) 14 (b) 11 (c) 10 (d) 100
19. 19.In which quadrant does the point (4, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
20. 20.In which quadrant does the point (−4, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
21. 21.In which quadrant does the point (−4, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
22. 22.What is the distance between the points (4, 23) and (16, 7)? (a) 28 (b) 400 (c) 21 (d) 20
23. 23.In which quadrant does the point (2, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
24. 24.What is the midpoint of the line joining (10, 10) and (12, 0)? (a) (1, 5) (b) (22, 10) (c) (5, 11) (d) (11, 5)
25. 25.What is the distance between the points (9, 5) and (13, 2)? (a) 25 (b) 7 (c) 6 (d) 5
26. 26.In which quadrant does the point (1, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
27. 27.What is the distance between the points (6, 1) and (21, 9)? (a) 23 (b) 289 (c) 17 (d) 18
28. 28.What is the distance between the points (0, 31) and (7, 7)? (a) 625 (b) 26 (c) 25 (d) 31
29. 29.What is the distance between the points (2, 6) and (18, 18)? (a) 20 (b) 400 (c) 21 (d) 28
30. 30.In which quadrant does the point (1, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
31. 31.What is the distance between the points (7, 19) and (16, 7)? (a) 21 (b) 16 (c) 225 (d) 15
32. 32.What is the midpoint of the line joining (9, 9) and (11, 19)? (a) (20, 28) (b) (1, 5) (c) (14, 10) (d) (10, 14)
33. 33.What is the midpoint of the line joining (4, 13) and (8, 7)? (a) (10, 6) (b) (2, 3) (c) (6, 10) (d) (12, 20)
34. 34.What is the midpoint of the line joining (10, 0) and (18, 2)? (a) (28, 2) (b) (4, 1) (c) (14, 1) (d) (1, 14)
35. 35.In which quadrant does the point (−5, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
36. 36.In which quadrant does the point (−2, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
37. 37.In which quadrant does the point (−7, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
38. 38.What is the distance between the points (1, 18) and (17, 6)? (a) 21 (b) 20 (c) 400 (d) 28
39. 39.In which quadrant does the point (5, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
40. 40.What is the midpoint of the line joining (1, 6) and (5, 4)? (a) (3, 5) (b) (2, 1) (c) (6, 10) (d) (5, 3)

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