This is the second quiz in our Difficult section on Position. It contains a mix of things you will have learned when you played our previous Eleven plus maths quizzes on the topic.

To get all the questions right you will need to understand the number of degrees in a complete rotation, a half rotation, a quarter rotation and an eighth of a rotation. You’ll also need to know all about where coordinates are placed on a graph and the difference between x and y axis, as well as the four quadrants.

Sounds like a lot doesn’t it? But, if you have played our easy and difficult quizzes, I’m sure you’ll breeze through it.

As always, take your time and read each question carefully before you choose your answer. Good luck!

1.

Which of the following is the angle between SW and N?

360^{o}

135^{o}

225^{o}

315^{o}

2.

Which direction does the straight line starting at (1, 1) and ending at (-1, 3) point in?

NE

N

NW

W

A diagram will help a lot in doing these questions!

3.

What are the coordinates of the point that is the same distance away from the y-axis as the point (4, 0)?

(-4, 0)

(0, 4)

(0, 0)

(2, 4)

(4, 0) is at 4 on the positive x-axis: 4 units to the right the y-axis. (-4, 0) is at -4 on the negative x-axis: 4 to the left of the y-axis

4.

You are facing SW. If you turn through 90^{o} anticlockwise and then 135^{o} clockwise, which direction will you be facing now?

NW

W

SW

S

'Anticlockwise' means that you turn (rotate) in the opposite direction to which the hands of the clock turn: the hands of the clock turn 'clockwise'. 90^{o} anticlockwise makes you face SE. Then, 135^{o} = three lots of 45^{o} clockwise, which makes you face W

5.

Which coordinates are SE of (1, 3)?

(-1, 5)

(1, -5)

(5, -1)

(-5, 1)

Starting at (1, 3) draw a line 135^{o} from North. All points along this line (including 5, -1) lie SE of (1, 3)

6.

You are facing E. If you turn through 315^{o} anticlockwise and then 225^{o} clockwise, which direction will you be facing now?

W

NW

N

NE

315^{o} anticlockwise = seven lots of 45^{o} (seven-eighths of a turn) makes you face SE. 225^{o} clockwise = 5 lots of 45^{o} = (five-eighths of a turn) makes you face N

7.

If you draw out a straight line path starting at A (1, 3) and move as follows: 5 cm E to point B, then SE to point C, which is due South of point A. From there you move 6 cm N to point E, where you stop. What are the coordinates of point E?

E = (1, 4)

E = (4, 4)

E = (4, 1)

E = (1, 1)

The best way to work this out is with a diagram – it’s very hard to keep all that information in your head!

8.

If you join up the points A (-2, 0), B (-2, 2), C (0, 2), D (0, 0) with straight lines you will get a square that lies in a certain quadrant. If the square is rotated anticlockwise through 90^{o} about the origin (0, 0), which quadrant will it end up in and what will its new coordinates be?

A (0, 2), B (2, 2), C (2, 0), D (0, 0) in the first quadrant

A (0, 2), B (-2, 2), C (-2, 0), D (0, 0) in the third quadrant

A (0, -2), B (2, -2), C (2, 0), D (0, 0) in the fourth quadrant

A (0, -2), B (-2, -2), C (-2, 0), D (0, 0) in the third quadrant

The square is initially in the second quadrant. Join up the four corners with straight lines (the lengths of which should be 2 units) to the centre 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!

9.

How many half rotations are there in 1,260^{o}?

7

9

12

14

There are 1,260^{o} ÷ 180^{o} = 7 half rotations

10.

A circle with centre (3, -3) and diameter 8 cm is drawn on the coordinate plane. Which points will the circle pass through?

(3, -1), (7, 3), (3, 7), (-1, -3)

(3, 1), (7, -3), (3, -7), (-1, -3)

(-3, 1), (-7, 3), (3, -7), (-1, -3)

(3, 1), (7, -3), (-3, 7), (1, -3)

The radius is half the diameter = 4 cm; therefore, the circle will pass through those points that are at a distance of 4 cm from its centre (3, -3)

^{o}which is the same as NW