The square grid below shows the positions of points A, B, C, D, E, F and G.

  1. (a)

    In what direction is point E from point B?

    Ans : ___

  2. (b)

    Kayel stood at one of the points facing C. After he turned 45∘45^\circ anti-clockwise, he faced G. Which point was Kayel at?

    Ans : Point ___

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Worked solution

23(a)

1. Determine the relative position of E from B on the grid

Point B is at column 3, row 1 (top border).
Point E is at column 5 (right border), row 3.
From B to E, the movement is 5−3=25 - 3 = 2 units to the right (East) and 3−1=23 - 1 = 2 units down (South).

2. Determine the compass direction based on the relative movement

Since the movement is equal units East and South (2 units each), the direction is exactly halfway between South and East, which is South-East.

Answer

South-East

23(b)

1. Understand the rotation and relative positions

Kayel turns 45∘45^\circ anti-clockwise from facing C to face G. This means the angle between the line of sight to C and the line of sight to G is 45∘45^\circ, with C being clockwise from G.

2. Test possible points for Kayel's position

Let's check the points. The angle between the line to C and the line to G must be 45∘45^\circ.
From D (row 3, col 4):

  • C is at (row 2, col 4), which is exactly North of D.
  • G is at (row 3, col 2), which is exactly West of D.
  • The angle between North (facing C) and West (facing G) is 90∘90^\circ, not 45∘45^\circ.
    From F (row 5, col 3):
  • C is at (row 2, col 4). Vector FC is 1 unit right, 3 units up.
  • G is at (row 3, col 2). Vector FG is 1 unit left, 2 units up.
  • The angle is not 45∘45^\circ.
    From A (row 2, col 1):
  • C is at (row 2, col 4), exactly East.
  • G is at (row 3, col 2), 1 unit right, 1 unit down (South-East).
  • The angle between East and South-East is 45∘45^\circ. If Kayel is at A facing C (East), turning 45∘45^\circ clockwise would face G. But the question says anti-clockwise.
    From E (row 3, col 5):
  • C is at (row 2, col 4), 1 unit left, 1 unit up (North-West).
  • G is at (row 3, col 2), exactly West.
  • Facing C (North-West) and turning 45∘45^\circ anti-clockwise brings the direction to West, which is exactly facing G.
Answer

D

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