Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 516 · 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 (5, 19) and (7, 7)? (a) (12, 26) (b) (1, 6) (c) (13, 6) (d) (6, 13)
2. 2.In which quadrant does the point (−3, −7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
3. 3.What is the midpoint of the line joining (0, 7) and (10, 11)? (a) (5, 2) (b) (10, 18) (c) (5, 9) (d) (9, 5)
4. 4.In which quadrant does the point (−9, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
5. 5.What is the midpoint of the line joining (4, 7) and (6, 15)? (a) (11, 5) (b) (10, 22) (c) (5, 11) (d) (1, 4)
6. 6.What is the midpoint of the line joining (0, 11) and (2, 7)? (a) (1, 9) (b) (2, 18) (c) (9, 1) (d) (1, 2)
7. 7.What is the distance between the points (3, 13) and (11, 7)? (a) 100 (b) 10 (c) 14 (d) 11
8. 8.What is the distance between the points (6, 4) and (21, 12)? (a) 289 (b) 23 (c) 17 (d) 18
9. 9.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
11. 11.What is the distance between the points (4, 0) and (16, 16)? (a) 28 (b) 21 (c) 400 (d) 20
12. 12.What is the distance between the points (7, 4) and (11, 7)? (a) 6 (b) 7 (c) 5 (d) 25
13. 13.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
14. 14.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
15. 15.What is the distance between the points (9, 4) and (16, 28)? (a) 26 (b) 25 (c) 625 (d) 31
16. 16.What is the distance between the points (5, 14) and (29, 7)? (a) 625 (b) 25 (c) 26 (d) 31
17. 17.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
18. 18.What is the distance between the points (8, 7) and (32, 14)? (a) 31 (b) 25 (c) 26 (d) 625
19. 19.In which quadrant does the point (6, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
20. 20.What is the midpoint of the line joining (4, 2) and (12, 8)? (a) (4, 3) (b) (8, 5) (c) (16, 10) (d) (5, 8)
21. 21.What is the distance between the points (6, 8) and (14, 14)? (a) 11 (b) 10 (c) 100 (d) 14
22. 22.What is the distance between the points (8, 1) and (11, 5)? (a) 5 (b) 6 (c) 25 (d) 7
23. 23.What is the midpoint of the line joining (7, 18) and (13, 6)? (a) (20, 24) (b) (12, 10) (c) (10, 12) (d) (3, 6)
24. 24.What is the distance between the points (8, 15) and (14, 7)? (a) 100 (b) 14 (c) 10 (d) 11
25. 25.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
26. 26.In which quadrant does the point (−5, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
27. 27.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
28. 28.What is the midpoint of the line joining (5, 5) and (13, 3)? (a) (18, 8) (b) (4, 9) (c) (9, 4) (d) (4, 1)
29. 29.What is the distance between the points (2, 3) and (26, 10)? (a) 26 (b) 625 (c) 25 (d) 31
30. 30.What is the distance between the points (7, 12) and (19, 7)? (a) 14 (b) 17 (c) 169 (d) 13
31. 31.What is the midpoint of the line joining (6, 3) and (18, 1)? (a) (6, 1) (b) (12, 2) (c) (24, 4) (d) (2, 12)
32. 32.What is the midpoint of the line joining (8, 8) and (20, 2)? (a) (14, 5) (b) (6, 3) (c) (28, 10) (d) (5, 14)
33. 33.What is the distance between the points (5, 3) and (8, 7)? (a) 7 (b) 5 (c) 25 (d) 6
34. 34.What is the distance between the points (3, 18) and (11, 3)? (a) 18 (b) 23 (c) 17 (d) 289
35. 35.What is the midpoint of the line joining (4, 6) and (6, 4)? (a) (10, 10) (b) (5, 5) (c) (6, 5) (d) (1, 1)
36. 36.What is the distance between the points (9, 5) and (15, 13)? (a) 11 (b) 100 (c) 10 (d) 14
37. 37.What is the distance between the points (9, 1) and (14, 13)? (a) 13 (b) 169 (c) 14 (d) 17
38. 38.What is the midpoint of the line joining (3, 14) and (13, 10)? (a) (16, 24) (b) (5, 2) (c) (8, 12) (d) (12, 8)
39. 39.What is the distance between the points (8, 4) and (11, 0)? (a) 6 (b) 5 (c) 25 (d) 7
40. 40.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17

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