Geometry - Position and Direction

What are the coordinates of point A on a grid where A is 3 units right and 2 units up from the origin?

• A(2, 2)
• B(3, 3)
• C(2, 3)
• D(3, 2)✓

Answer: Coordinates are written as (x, y). 3 units right = x-coordinate of 3. 2 units up = y-coordinate of 2. So the point is (3, 2).

If you face north and turn 90° clockwise, which direction do you face?

• ANorth-West
• BWest
• CSouth
• DEast✓

Answer: Turning 90° clockwise from north takes you to the east.

What are the coordinates of a point that is 4 units left and 3 units down from the origin?

• A(-4, -3)✓
• B(-4, 3)
• C(4, -3)
• D(4, 3)

Answer: 4 units left = x-coordinate of -4. 3 units down = y-coordinate of -3. So the point is (-4, -3).

If you face south and turn 180°, which direction do you face?

• ANorth✓
• BWest
• CSouth-East
• DEast

Answer: Turning 180° from any direction takes you to the opposite direction. The opposite of south is north.

What is the coordinate that is 2 units right and 4 units up from the point (3, 1)?

• A(5, 5)✓
• B(5, 3)
• C(3, 5)
• D(1, -3)

Answer: (3, 1) + (2, 4) = (3+2, 1+4) = (5, 5).

On a square grid, which point is at coordinates (2, 0)?

• A2 units up
• B2 units right✓
• COn the y-axis
• D2 units left

Answer: (2, 0) means x-coordinate of 2 and y-coordinate of 0. This is 2 units right on the x-axis.

If you face west and turn 90° anti-clockwise (counter-clockwise), which direction do you face?

• ANorth
• BEast
• CSouth✓
• DWest

Answer: Turning 90° anti-clockwise from west takes you to south.

A shape has vertices at (0, 0), (4, 0), (4, 3), and (0, 3). What shape is it?

• AA trapezium
• BA triangle
• CA pentagon
• DA rectangle✓

Answer: These four points form a rectangle with width 4 and height 3.

What is the coordinate of the origin?

• A(1, 1)
• B(0, 1)
• C(1, 0)
• D(0, 0)✓

Answer: The origin is where the x-axis and y-axis meet, at coordinates (0, 0).

If a point is at (5, 3), how many units is it to the right of the y-axis?

• A15 units
• B8 units
• C3 units
• D5 units✓

Answer: The x-coordinate tells you the distance from the y-axis. The point (5, 3) is 5 units to the right.

You are at position (2, 2). You move 3 units right and 1 unit down. What is your new position?

• A(5, 1)✓
• B(5, 3)
• C(-1, 1)
• D(5, 2)

Answer: (2, 2) + (3 right, 1 down) = (2+3, 2-1) = (5, 1).

How many degrees is a full turn?

• A180°
• B90°
• C360°✓
• D270°

Answer: A full turn is 360°.

A ship travels from position (1, 2) to position (6, 2). In which direction did it travel?

• AEast✓
• BSouth
• CWest
• DNorth

Answer: The y-coordinate stayed at 2, but the x-coordinate increased from 1 to 6. This means moving right, which is east.

If you turn 270° clockwise, it's the same as turning 90° in which direction?

• AClockwise
• BEither direction
• CNeither direction
• DAnti-clockwise✓

Answer: A full turn is 360°, and 360° − 270° = 90°. So turning 270° clockwise leaves you facing the same way as turning 90° anti-clockwise.

On a coordinate grid, the point (3, 4) is reflected across the x-axis. What are the new coordinates?

• A(4, 3)
• B(-3, 4)
• C(-3, -4)
• D(3, -4)✓

Answer: Reflection across the x-axis changes the sign of the y-coordinate. (3, 4) becomes (3, -4).

If you face north and turn 90° clockwise, which direction are you now facing?

• ANorth
• BSouth
• CWest
• DEast✓

Answer: Turning 90° clockwise from north brings you to face east.

A shape is reflected across a vertical line. What type of transformation is this?

• AEnlargement
• BTranslation
• CRotation
• DReflection✓

Answer: Reflecting a shape means flipping it across a line.

If you are at point (3, 2) and move 2 units right and 1 unit up, where do you end up?

• A(1, 1)
• B(3, 4)
• C(5, 1)
• D(5, 3)✓

Answer: Starting at (3, 2), moving 2 units right gives 3 + 2 = 5, and 1 unit up gives 2 + 1 = 3, so you end up at (5, 3).

If you face south and turn 180°, which direction are you now facing?

• ASouth
• BNorth✓
• CEast
• DWest

Answer: Turning 180° from south brings you to face north.

A shape is rotated 90° clockwise. What happens to its position?

• AIt slides across without turning
• BIt flips over a mirror line
• CIt turns around a fixed point✓
• DIt becomes larger in size

Answer: Rotation turns a shape around a fixed point called the centre of rotation. The shape keeps its size, and it is neither flipped nor slid.

Which of the following is a translation?

• AFlipping a shape
• BTurning a shape
• CEnlarging a shape
• DSliding a shape✓

Answer: A translation is when a shape slides from one position to another without rotating or flipping.

If you are at coordinates (1, 4) and move 3 units left, where are you?

• A(1, 1)
• B(-2, 4)✓
• C(1, 7)
• D(4, 4)

Answer: Starting at (1, 4), moving 3 units left means 1 - 3 = -2, so you are at (-2, 4).

If you face east and turn 90° anti-clockwise, which direction are you now facing?

• AEast
• BSouth
• CWest
• DNorth✓

Answer: Turning 90° anti-clockwise from east brings you to face north.

What type of transformation makes a shape twice as large?

• ATranslation
• BReflection
• CRotation
• DEnlargement✓

Answer: An enlargement makes a shape bigger or smaller.

If you are at (5, 5) and move to (5, 2), how many units down did you move?

• A1 unit
• B2 units
• C3 units✓
• D5 units

Answer: Moving from (5, 5) to (5, 2) means the y-coordinate changed from 5 to 2, a change of 5 - 2 = 3 units down.

A shape has rotational symmetry of order 4. How many times can it be rotated to look the same (including 360°)?

• A2
• B3
• C4✓
• D5

Answer: Rotational symmetry of order 4 means the shape looks the same when rotated 4 times in a full 360° turn.

If you face west and turn 270° clockwise, which direction are you now facing?

• AWest
• BEast
• CSouth✓
• DNorth

Answer: A full turn is 360°, so turning 270° clockwise leaves you facing the same way as turning 90° anti-clockwise. From west that brings you to face south.

On a coordinate grid, point A is at (2, 3) and point B is at (5, 3). What is the horizontal distance between them?

• A1 unit
• B2 units
• C3 units✓
• D5 units

Answer: Both points have the same y-coordinate (3), so the distance is the difference in x-coordinates: 5 - 2 = 3 units.

A shape has line symmetry. What does this mean?

• AIt can be flipped across a line and look the same✓
• BIt can be enlarged
• CIt can be translated
• DIt can be rotated

Answer: Line symmetry means a shape can be folded along a line so that both halves match exactly.

If you travel 4 km north and then 4 km east, which direction is the straight-line path from your starting point?

• ANorth
• BEast
• CNorth-west
• DNorth-east✓

Answer: Travelling the same distance north and then east leaves you exactly halfway between north and east, which is north-east.