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Knowing the compass points will help when playing this quiz.
Position 4
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?
1 .
How many complete rotations are there in 3,249°?
9
7
12
8
There are 3,249° ÷ 360° = 9 complete rotations
2 .
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
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!
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
'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 .
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)
5 .
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
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
6 .
Which of the following is the angle between NE and S?
315°
45°
225°
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°
7 .
What are the coordinates of the point that is the same distance away from the x-axis as the point
(0, 5)?
(0, 5)?
(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
8 .
Which direction does the straight line starting at (0, 0) and ending at (6, 6) point in?
NW
SE
NE
E
A diagram will help a lot in doing these questions
9 .
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)
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)
10 .
Which coordinates are NW of (3, -3)?
(3, 3)
(-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)
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