The idea in brief. Every constraint here is exact and none of them can be judged by eye on a slanted line. A parallel side is the same run and the same rise; twice as long is both of them doubled; a right angle is the two swapped. Count it.
Lesson video, with the working
Drawing on a grid
3 min 22 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
The dot grid below has A at (4, 4), B at (2, 1) and C at (8, 6). Draw the trapezium ABYC, in which BY is parallel to AC and BY is twice as long as AC. Write down the coordinates of Y.
Y is at (10, 5).
Ans: (10, 5)
Example 1
The 1-cm square grid below shows the rhombus PQRS, with P at (1, 4), Q at (5, 1), R at (9, 4) and S at (5, 7). Draw the square RSUV on the side RS, so that the square does not overlap the rhombus. Write down the coordinates of U and V.
U is at (8, 11)
and V is at (12, 8).
Ans: (8, 11)(12, 8)
How to solve it
Count squares, across then up. A to C is 4 squares right and 2 squares up.
For a parallel side, walk the same run and rise from B. Twice as long means 8 squares right and 4 up.
Read the coordinates of the end point: Y is at 10, 5.
For a right angle, swap run and rise: R S is 4 left, 3 up, so a quarter turn is 3 right, 4 up.
Choose the side the question wants. The square must not overlap the rhombus, so build it 3 right and 4 up.
A parallel side is the same run and the same rise. A right angle is those two swapped. And the question says which side of the line.
Practice questions with worked solutions
Question 1 is free to try. The other 5 open in the free trial, each with its full working.
Question 1 of 6 · Basic · free to tryThe grid below is a 1-cm square grid. The sides PQ and QR of a rhombus PQRS…The grid below is a 1-cm square…
The grid below is a 1-cm square grid. The sides PQ and QR of a rhombus PQRS have been drawn on it, with P at (1, 4), Q at (5, 1) and R at (9, 4). Complete the rhombus PQRS and write down the coordinates of S.
QR runs 4 squares right and 3 squares up, so QR is the same length as PQ
in a rhombus SR is parallel to PQ and the same length, so S is 4 squares left and 3 squares up from R
R is at (9, 4), so S is at (5, 7)
PS runs 4 squares right and 3 squares up from P and reaches the same point, so all four sides are equal and PQRS is a rhombus
Answer: S at (5, 7)
For parents
How do you answer drawing shapes on a grid questions in P6?
Here a child completes a square, rhombus, trapezium or triangle on a square or dot grid so that it meets exact conditions: parallel sides, right angles, equal lengths.
What your child learns here
Here a child completes a square, rhombus, trapezium or triangle on a square or dot grid so that it meets exact conditions: parallel sides, right angles, equal lengths. There is no separate Primary 6 learning outcome for grid drawing. These questions apply geometry outcomes from earlier years, drawing parallel and perpendicular lines and the properties of special quadrilaterals, in the form they take in P6 exam papers.
Describe a slanted side as a run across and a rise up, counted in squares.
Draw a parallel side by repeating the same run and rise from a new point.
Make a side twice or half as long by doubling or halving both counts.
Make a right angle by swapping the run and the rise and turning one of them round.
Use the properties of squares, rhombuses, trapeziums and right-angled triangles to decide where each corner goes.
Does the answer make sense?
Every corner your child adds must sit exactly on a dot or grid crossing, so its coordinates are whole numbers. In a square, the across and up counts of one side reappear in the next side swapped, with one direction turned round, while opposite sides of a parallelogram or rhombus repeat exactly the same counts.
How to practise these questions
The Basic questions train drawing shapes such as a rhombus on a grid, and turning a line through a quarter turn. Intermediate questions add drawing parallel lines by counting across and up. Challenge questions require two conditions to hold at once, the diagonals of a square, or more than one possible fourth corner. If drawing on the grid goes off course, read the written step-by-step solution together.
Questions parents ask
What is the difference between a square grid and a dot grid? A square grid is ruled into squares; a dot grid shows only the corners. Both are counted the same way, in steps from one point to the next.
How do you draw a right angle on a grid without a protractor? Count the first side as a run across and a rise up, then swap the two numbers and turn one of them round. A side of 3 right and 1 up meets a side of 1 left and 3 up at a right angle.
Is drawing on a grid in the P6 syllabus? There is no separate Primary 6 outcome for it. The skills come from earlier years: drawing perpendicular and parallel lines, drawing rectangles and squares, and the properties of the parallelogram, rhombus and trapezium.
