Week 09 · Coordinates: Lines, Segments and Figures
Shop Day
Shop Day: a grid at home
// The taped stage grid
⏱ about 20 min
Shop Day: A Grid at Home
Comet hands Wren a fresh roll of masking tape at the shop door. "Shop Day. A grid on your floor, as big as fits."
"One corner is the origin," Wren says. "Two tapes are the axes. Every mark gets coordinates from the tape measure."
"Then four marks for a platform," Comet says. "Prove it is a rectangle, or find out it is not."
Nova dims to a soft glow. "Would you like a hint? Measure each mark twice, once from each axis."
"Our designer, your family is the stage crew," Comet says. "One measures, one writes, one checks the slopes."
"And the tape comes up after," Wren adds. "Floors are borrowed."
- Slope = change in y ÷ change in x. Equal slopes: parallel. Product -1: perpendicular.
- Midpoint: average the endpoints. Partition a:b: go a ÷ (a + b) of the way.
- Distance = square root of (change in x)² + (change in y)², the Pythagorean theorem.
- Rectangle proof: parallel opposite sides, then one right angle, then all four. Diagonals equal as a check.
- Perimeter: add the distances. Area: base × height, or box and subtract.
◇ TAPE A GRID, PROVE A PLATFORM
Tape two straight axes along a floor corner. Mark every half meter on each with a pen on the tape.
Lay four small tape marks where you think a rectangle's corners should go. Measure each mark's coordinates.
Together, find the slope of each side and the length of both diagonals. Does it pass the rectangle test?
Find the midpoint of one diagonal, then of the other. In a rectangle they should be the same point. Check on the floor.
Lay four small tape marks where you think a rectangle's corners should go. Measure each mark's coordinates.
Together, find the slope of each side and the length of both diagonals. Does it pass the rectangle test?
Find the midpoint of one diagonal, then of the other. In a rectangle they should be the same point. Check on the floor.
For a grown-up
Masking tape on a hard floor lifts cleanly within the day. Test a corner first on wood or carpet.
Clear the space together; nothing heavy is moved by one person.
Half-meter marks are plenty. A phone calculator handles the square roots.
Clear the space together; nothing heavy is moved by one person.
Half-meter marks are plenty. A phone calculator handles the square roots.
GRID CHECK
- Read the question.
- Tap your answer.
The platform's diagonal AC runs from (1, 1) to (6, 6). What is its midpoint?
The other diagonal BD runs from (7, 3) to (0, 4). What is its midpoint?Your first two sides run from (0, 0) to (6, 2) and from (6, 2) to (5, 5). Parallel, perpendicular or neither?
Draw your home grid with your four marks. Label each mark's coordinates and each side's slope.
A platform proved on a borrowed floor. Next week the turntable circle gets its own equation on the stage grid.