Drawing on a grid

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. Try it first. Pause if you like. Count the squares. Count across, then count up. From A, count 4 squares right. Then count 2 squares up to C. A C is 4 right and 2 up. Start the same walk from B. This new segment is parallel to A C. But B Y is twice as long as A C. Double both counts: 8 right and 4 up. From B, count 8 squares right. Then count 4 squares up. Join this point to C. A C and B Y are the one pair of parallel sides. So Y is at (10, 5). The same run and rise make a parallel side. Doubling both makes it twice as long.

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. Draw it on paper, then compare. Try it first. Pause if you like. The question builds the square on side R S, so R S is the square's first side. From R, count 4 squares left. Then count 3 squares up to S. Side R S is 4 left and 3 up. Every corner of a square is a right angle, so the next side must turn through one right angle. A quarter turn is a turn through one right angle. Swing a copy of the side round the corner at S. One quarter turn goes 3 squares right and 4 squares up. The other goes 3 squares left and 4 squares down. This overlaps with the rhombus, which is not what the question wants. So the square is built 3 right and 4 up. From S, count 3 squares right. Then count 4 squares up. U is at (8, 11). A square's opposite sides are equal and parallel. So from R, count the same 3 squares right. Then count the same 4 squares up. V is at (12, 8). Join U to V to close the square. A parallel side has the same run and the same rise. For a right angle, swap the counts and turn the direction. And the question says which side of the line.