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Math: Middle School: Grades 6, 7 and 8 Quiz - Position 4 (Questions)

This Math quiz is called 'Position 4' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.

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In this middle school Math quiz on position you'll get a chance to see what you remember about the coordinate plane and the compass. Did you know that the coordinate plane is also called the Cartesian plane?

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Did you know that map directions are given using bearings? Some people use a 'thumb compass' when reading maps. These are very basic compasses that normally only show magnetic north. They are used in orienteering. But if a compass is held over a map, how can people read what is underneath the map? Can you figure it out? It's easy really - the compasses are transparent so that the map-readers can see right through!

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1. Which direction does the straight line starting at (0, 0) and ending at (6, 6) point in?
[ ] NW
[ ] SE
[ ] NE
[ ] E
2. What are the coordinates of the point that is the same distance away from the x-axis as the point
(0, 5)?
[ ] (0, -5)
[ ] (-5, 0)
[ ] (5, 0)
[ ] (5, 5)
3. You are facing NE. If you turn through 180° counterclockwise and then 135° clockwise, which direction will you be facing now?
[ ] N
[ ] NW
[ ] NE
[ ] E
4. You are facing NW. If you turn through 315° counterclockwise and then 225° clockwise, which direction will you be facing now?
[ ] W
[ ] E
[ ] NE
[ ] SW
5. Which of the following is the angle between NE and S?
[ ] 315°
[ ] 45°
[ ] 225°
[ ] 135°
6. If you join up the points A (0, 0), B (1, 0), C (1, -1), D (0, -1) with straight lines you will get a square that lies in a certain quadrant. If the square is rotated counterclockwise through 90° about the origin (0, 0), which quadrant will it end up in and what will its new coordinates be?
[ ] A (0, 0), B (1, 0), C (1, -1), D (0, 1) in the first quadrant
[ ] A (0, 0), B (0, 1), C (1, 1), D (1, 0) in the first quadrant
[ ] A (0, 0), B (0, -1), C (-1, -1), D (-1, 0) in the third quadrant
[ ] A (0, 0), B (1, 0), C (0, -1), D (-1, -1) in the third quadrant
7. Eddie is tracing out a straight line path in the Cartesian plane. He starts at A (0, 0) and moves as follows: 3 cm E to point B, then NW to point C, which is due North of point A. From there he moves the same distance SW to point D, and finally 6 cm S to point E, where he stops. What are the coordinates of point E?
[ ] E (-3, 6)
[ ] E (3, -6)
[ ] E (-3, -6)
[ ] E (3, 6)
8. How many complete rotations are there in 3,249°?
[ ] 9
[ ] 7
[ ] 12
[ ] 8
9. Which coordinates are NW of (3, -3)?
[ ] (3, 3)
[ ] (-3, 3)
[ ] (-3, -3)
[ ] (3, -3)
10. A circle with center (0, 0) and diameter 6 cm is drawn on the coordinate plane. Which points will the circle pass through?
[ ] (3, 0), (0, 3), (-3, 0), (0, -3)
[ ] (6, 0), (0, 6), (-6, 0), (0, -6)
[ ] (6, 0), (6, 6), (-6, 0), (0, -6)
[ ] (6, 0), (0, 6), (-6, -6), (0, -6)
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Math: Middle School: Grades 6, 7 and 8 Quiz - Position 4 (Answers)
1. Which direction does the straight line starting at (0, 0) and ending at (6, 6) point in?
[ ] NW
[ ] SE
[x] NE
[ ] E
A diagram will help a lot in doing these questions
2. What are the coordinates of the point that is the same distance away from the x-axis as the point
(0, 5)?
[x] (0, -5)
[ ] (-5, 0)
[ ] (5, 0)
[ ] (5, 5)
(0, 5) is at 5 on the positive y-axis: 5 units above the x-axis. (0, -5) is at -5 on the negative y-axis: 5 below the x-axis
3. You are facing NE. If you turn through 180° counterclockwise and then 135° clockwise, which direction will you be facing now?
[x] N
[ ] NW
[ ] NE
[ ] E
'Counterclockwise' means that you turn (rotate) in the opposite direction to which the hands of the clock turn: the hands of the clock turn 'clockwise'. 180° = two lots of 90° (a half turn) counterclockwise makes you face SW. 135° clockwise = 3 lots of 45° = three-eighths of a turn makes you face N
4. You are facing NW. If you turn through 315° counterclockwise and then 225° clockwise, which direction will you be facing now?
[ ] W
[ ] E
[ ] NE
[x] SW
315° counterclockwise = seven lots of 45° (seven-eighths of a turn) makes you face N. 225° clockwise = 5 lots of 45° = (five-eighths of a turn) makes you face SW
5. Which of the following is the angle between NE and S?
[ ] 315°
[ ] 45°
[ ] 225°
[x] 135°
Three lots of 45°. If you rotated in the counterclockwise direction, it would be five lots of 45° = 225°. Whenever you can, always give the smallest angle. Note: 225° counterclockwise + 135° clockwise = 360°
6. If you join up the points A (0, 0), B (1, 0), C (1, -1), D (0, -1) with straight lines you will get a square that lies in a certain quadrant. If the square is rotated counterclockwise through 90° about the origin (0, 0), which quadrant will it end up in and what will its new coordinates be?
[ ] A (0, 0), B (1, 0), C (1, -1), D (0, 1) in the first quadrant
[x] A (0, 0), B (0, 1), C (1, 1), D (1, 0) in the first quadrant
[ ] A (0, 0), B (0, -1), C (-1, -1), D (-1, 0) in the third quadrant
[ ] A (0, 0), B (1, 0), C (0, -1), D (-1, -1) in the third quadrant
The square is initially in the fourth quadrant. Join up the four corners with straight lines (the lengths of which should be 1 unit) to the center of rotation (0, 0). Now rotate the lines and watch where their end points end up: these will give you the positions of the new coordinates of the square. Draw it!
7. Eddie is tracing out a straight line path in the Cartesian plane. He starts at A (0, 0) and moves as follows: 3 cm E to point B, then NW to point C, which is due North of point A. From there he moves the same distance SW to point D, and finally 6 cm S to point E, where he stops. What are the coordinates of point E?
[ ] E (-3, 6)
[ ] E (3, -6)
[x] E (-3, -6)
[ ] E (3, 6)
A (0, 0), B (3, 0), C (0, 4), D (-3, 0), E (-3, -6). ABC is a right triangle: 3, 4, 5: that's how you know that D is (0, 4). Draw it!
8. How many complete rotations are there in 3,249°?
[x] 9
[ ] 7
[ ] 12
[ ] 8
There are 3,249° ÷ 360° = 9 complete rotations
9. Which coordinates are NW of (3, -3)?
[ ] (3, 3)
[x] (-3, 3)
[ ] (-3, -3)
[ ] (3, -3)
(3, -3) is SE of (0, 0). Join up (0, 0) and (3, -3) with a straight line and rotate the line about (0, 0) through 180° to get to NW: you should end up at (-3, 3)
10. A circle with center (0, 0) and diameter 6 cm is drawn on the coordinate plane. Which points will the circle pass through?
[x] (3, 0), (0, 3), (-3, 0), (0, -3)
[ ] (6, 0), (0, 6), (-6, 0), (0, -6)
[ ] (6, 0), (6, 6), (-6, 0), (0, -6)
[ ] (6, 0), (0, 6), (-6, -6), (0, -6)
The radius is half the diameter = 3 cm; therefore, the circle will pass through those points that are at a distance of 3 cm from its center (0, 0)
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