Coordinate Transformations
Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original
What a learner can do afterwards
- Reflect a shape in a given mirror line (including diagonal lines) and state the coordinates of the image
- Rotate a shape about a given centre by 90 or 180 degrees and describe the result
- Translate a shape by a given vector and verify that lengths and angles are preserved
- Update both coordinates by the horizontal and vertical increments of a translation
- Reflect across x = c by keeping y and placing x the same distance on the other side
1 · Read
You already know how to slide a shape and flip it on a grid. A rotation turns a shape around a fixed point. These moves do not stretch or squash a shape, so side lengths and angles stay the same.
To reflect a point in the diagonal line y = x, swap its two coordinates. Point (2, 5) becomes (5, 2).
A 180 degree rotation about the origin changes (x, y) to (-x, -y). A 90 degree clockwise rotation changes (x, y) to (y, -x).
A translation changes coordinates by its movement. Moving right adds to x, moving left subtracts from x, moving up adds to y, and moving down subtracts from y. A reflection in x = c keeps y and places x the same distance on the other side.
A reflection in y = x swaps the coordinates. For example, (-6, 2) becomes (2, -6). The point has the same distance from the mirror line on each side.
For a 90 degree clockwise turn about the origin, swap coordinates and make the second coordinate negative. For example, (6, 2) becomes (2, -6). A half-turn changes both signs.
Reflections, rotations, and translations move a shape to a new position without changing its size or angles.
Extra items x1-x4 are original rewrites from this source pass. Retained items x5-x10 keep their Khan Academy article or video credit.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.