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