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Primary 6 · Solids · Question type 10.4

P6 Solids: Drawing Shapes on a Grid

Count a slanted side as a run and rise in squares. A parallel side repeats both, a side twice as long doubles both, and a right angle swaps them.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Solids chapter4 question types · see the chapter

The lesson · 3 minutes 29 seconds

How do you draw shapes on a square or dot grid in P6?

Watch: the trapezium ABYC, with BY parallel to AC and twice as long

Another worked example

A worked example

The dot grid below has A at (2, 3) and B at (8, 5). Draw the trapezium ABCD, in which DC is parallel to AB, AD is at right angles to AB, and AD and DC are each half as long as AB. D is above the line AB. Write down the coordinates of C and D.

The working · Seven lines

The step-by-step working

Written out in full, the way it should appear on paper.

  1. AB runs 6 squares right and 2 squares up
  2. half of AB is 3 squares right and 1 square up
  3. AD is at right angles to AB and half as long, so AD runs 1 square left and 3 squares up
  4. A is at (2, 3), so D is at (1, 6)
  5. DC is parallel to AB and half as long, so DC runs 3 squares right and 1 square up
  6. D is at (1, 6), so C is at (4, 7)
  7. AB and DC are parallel and of different lengths, so ABCD is a trapezium, and the angles at A and at D are right angles

The answer is D at (1, 6) and C at (4, 7).

Practise · Modelled on top school exam questions

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Complete the symmetric figure

Reflect the given part across the line of symmetry and compare your drawing with the solution.

The square grid below shows part of a figure and its line of symmetry, the broken line through x = 6. The part drawn goes from (6, 2) to (2, 2) to (2, 7) to (4, 10) to (6, 10). Complete the symmetric figure and write down the coordinates of the three new corners.

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Show the step-by-step solution
  1. the line of symmetry is the line x = 6
  2. the corner (2, 2) is 4 squares left of the line, so its mirror image is 4 squares right of it, at (10, 2)
  3. the corner (2, 7) is 4 squares left of the line, so its mirror image is at (10, 7)
  4. the corner (4, 10) is 2 squares left of the line, so its mirror image is at (8, 10)
  5. the corners (6, 2) and (6, 10) are on the line itself, so they do not move
  6. joining (6, 10) to (8, 10) to (10, 7) to (10, 2) to (6, 2) completes the figure

Ans: the new corners are at (8, 10), (10, 7) and (10, 2)

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