Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 439 · 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.What is the midpoint of the line joining (3, 6) and (13, 16)? (a) (11, 8) (b) (5, 5) (c) (16, 22) (d) (8, 11)
2. 2.In which quadrant does the point (−1, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
3. 3.In which quadrant does the point (6, 9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
4. 4.What is the midpoint of the line joining (9, 6) and (19, 0)? (a) (3, 14) (b) (14, 3) (c) (28, 6) (d) (5, 3)
5. 5.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
6. 6.In which quadrant does the point (−4, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
7. 7.What is the distance between the points (4, 22) and (16, 6)? (a) 20 (b) 28 (c) 400 (d) 21
8. 8.In which quadrant does the point (−4, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
9. 9.What is the midpoint of the line joining (6, 3) and (10, 13)? (a) (9, 8) (b) (16, 16) (c) (8, 8) (d) (2, 5)
10. 10.In which quadrant does the point (8, −7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
11. 11.What is the midpoint of the line joining (10, 8) and (16, 6)? (a) (3, 1) (b) (26, 14) (c) (7, 13) (d) (13, 7)
12. 12.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
13. 13.What is the distance between the points (8, 2) and (20, 11)? (a) 225 (b) 21 (c) 16 (d) 15
14. 14.What is the midpoint of the line joining (2, 3) and (8, 5)? (a) (3, 1) (b) (4, 5) (c) (10, 8) (d) (5, 4)
15. 15.In which quadrant does the point (8, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
16. 16.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
17. 17.What is the midpoint of the line joining (7, 7) and (9, 1)? (a) (4, 8) (b) (8, 4) (c) (16, 8) (d) (1, 3)
18. 18.What is the distance between the points (3, 24) and (11, 9)? (a) 289 (b) 18 (c) 23 (d) 17
19. 19.In which quadrant does the point (−1, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
20. 20.What is the distance between the points (7, 13) and (16, 1)? (a) 225 (b) 15 (c) 16 (d) 21
21. 21.What is the distance between the points (2, 9) and (8, 17)? (a) 100 (b) 11 (c) 14 (d) 10
22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
23. 23.What is the distance between the points (3, 11) and (7, 8)? (a) 7 (b) 6 (c) 5 (d) 25
24. 24.What is the distance between the points (9, 15) and (24, 7)? (a) 289 (b) 23 (c) 17 (d) 18
25. 25.What is the distance between the points (8, 12) and (20, 7)? (a) 17 (b) 13 (c) 169 (d) 14
26. 26.In which quadrant does the point (−7, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
27. 27.In which quadrant does the point (7, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
28. 28.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
29. 29.In which quadrant does the point (−3, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
30. 30.In which quadrant does the point (−2, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
31. 31.In which quadrant does the point (7, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
32. 32.What is the midpoint of the line joining (0, 19) and (2, 9)? (a) (2, 28) (b) (1, 14) (c) (14, 1) (d) (1, 5)
33. 33.What is the distance between the points (7, 16) and (13, 8)? (a) 14 (b) 100 (c) 10 (d) 11
34. 34.What is the distance between the points (3, 21) and (11, 6)? (a) 18 (b) 23 (c) 289 (d) 17
35. 35.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
36. 36.What is the midpoint of the line joining (8, 7) and (10, 3)? (a) (5, 9) (b) (18, 10) (c) (1, 2) (d) (9, 5)
37. 37.In which quadrant does the point (5, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
38. 38.What is the distance between the points (2, 9) and (14, 25)? (a) 400 (b) 21 (c) 28 (d) 20
39. 39.What is the distance between the points (1, 11) and (4, 7)? (a) 7 (b) 25 (c) 6 (d) 5
40. 40.What is the midpoint of the line joining (1, 10) and (3, 18)? (a) (2, 14) (b) (4, 28) (c) (14, 2) (d) (1, 4)

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