Success criteria
- I plot and connect points in the stated order.
- I apply a translation, reflection, and quarter-turn rotation.
- I verify that an isometric image is congruent to the original.
Learn and explain
Plot rectangle ABCD on a paper grid with axes centered at the origin:
| Point | Coordinate |
|---|---|
| A | (-3, -2) |
| B | (2, -2) |
| C | (2, 2) |
| D | (-3, 2) |
The rectangle reaches into every quadrant. Its horizontal and vertical side lengths come from coordinate differences, making the perimeter 18 units. Explain why signed coordinates do not make a side length negative.
A translation adds the same signed change to every point. A reflection mirrors points across a line. A rotation turns them around a centre. These are isometric transformations: distances and angles stay unchanged, so the image remains congruent to the original even when position or orientation changes.
Independent practice
Find the perimeter of rectangle ABCD.
Coordinate differences give the two side lengths, so the perimeter is 18 units.
Point C is translated by (-4, 3). What are its new coordinates?
C moves to (-2, 5).
Point B is reflected across the y-axis. What is its image?
Reflection across the y-axis changes the sign of x, giving (-2, -2).
Point A rotates one quarter-turn clockwise about the origin. What is its image?
A clockwise quarter-turn maps it to (-2, 3).
Unfamiliar transfer — Coordinate Battleship (paper fallback)
This is paper-first. On two hidden four-quadrant grids with centered axes, each player draws several axis-aligned ships that may cross quadrants. Call one ordered pair per turn and mark hit or miss. After play, write the coordinates of one ship and explain how signs and coordinate order locate it.
The activity is only a coded-game candidate after the core course is on schedule; this lesson does not require software.
Then create a small logo that uses all four quadrants. Produce three congruent images: one translation, one reflection, and one quarter-turn rotation. List original/image coordinate pairs and explain which properties stayed fixed.
Delayed check
One to two weeks later, reproduce the logo from only its ordered-pair list and apply one randomly chosen isometric transformation. Check every image point and explain why the result is congruent rather than merely similar.
Evidence path
Save the original and translated coordinate designs to jeremy/portfolio/math/unit-5/lesson-16-coordinate-design/ with a short explanation of two shape relationships.
Next step
- Repair: if plotting errors remain, replay one paper round with axes and signs highlighted.
- Continue: if all three transformations are independent and verified, complete the Unit 5 mixed check.
- Stretch: combine transformations and predict whether their order changes the final image.