A copy is the same shape and size
A copy of a figure has every side the same length as the figure, and every corner turning the same way. The copy can sit anywhere on the grid, but it must not be longer, shorter or turned around.
On a dot grid, measure a side by counting the gaps between the dots, not the dots themselves. The top side of this figure starts at one dot and ends 3 dots along, so it is 3 gaps long. It touches 4 dots, and counting the dots is the usual mistake: it makes every side one gap too long.
The top side is 3 gaps long and the right side is 1 gap long. Then the figure turns left for 2 gaps, down for 1 gap and left for 1 gap, and the left side runs 2 gaps back up to the start.
Copy it one side at a time
Choose a starting dot for the copy, here 5 dots to the right of the figure's top-left corner. Then walk around the figure and copy each side in turn. The figure's top side goes 3 gaps to the right, so the copy's top side goes 3 gaps to the right from its starting dot.
Next the figure turns down for 1 gap, so the copy turns down for 1 gap. Keep going: left 2 gaps, down 1 gap, left 1 gap, and up 2 gaps. Each side of the copy has the same count of gaps as the side it copies, and it goes the same way.
The copy's top side is drawn: 3 gaps, the same as the figure's top side.
The finished copy has the same six sides as the figure, each the same number of gaps long.
Check that it closes
The last side of the copy should end exactly on the dot where the copy started. If it ends one dot short or one dot past, a side was miscounted, so count the gaps on each side again and compare them with the figure.
Moving a figure to a new place on the grid does not change its size. A copy drawn lower or further along is still the same number of gaps wide and the same number of gaps tall.
Worked example: A Figure Copied One Row Lower on a Square Grid
Question Mei draws a rectangle on a square grid. The rows of the grid are numbered from the top. The rectangle is 3 squares wide and 2 squares tall. Its top row is row 2. Mei draws a copy next to it, 1 row lower. (a) How many grid squares does the copy cover? (b) Which row is the top row of the copy?
1.Draw the rectangle on the grid. It has 2 rows, and each row has 3 squares.
The rectangle has 2 rows, and each row has 3 squares. Its top row is row 2. 2.Count the squares it covers: 3 + 3 = 6 squares.
Count the squares it covers: 3 + 3 = 6 squares. 3.(a) The copy is the same size as the figure. It is also 3 squares wide and 2 squares tall, so the copy covers 6 squares.
(a) The copy is the same size as the figure, so it covers 6 squares. 4.(b) The copy is 1 row lower, so its top row moves from row 2 to row 2 + 1 = 3. The top row of the copy is row 3.
(b) The copy is 1 row lower. Its top row is row 2 + 1 = 3.
Answer: (a) 6 squares; (b) row 3
Common mistakes
- Drawing the copy 3 squares tall because it is lower on the grid. Moving a figure does not change its size. The copy is still 2 squares tall.
- Writing row 1 for part (b). The rows are numbered from the top, so a lower row has a bigger number. Add 1 to the row number.