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° and describe the result
- Translate a shape by a given vector and verify that lengths and angles are preserved
The lesson
You already know how to slide a shape (translate it) and flip it (reflect it) on a grid. Now you'll add a third move: turning a shape around a fixed point, called a rotation. All three moves pick a shape up and set it down somewhere else without stretching or squashing it. The new shape is called the image, and it is always congruent to the original: same side lengths, same angles, just in a new spot.
To reflect a point in the diagonal line y = x, swap its two coordinates. Point (2, 5) becomes (5, 2). Point (-2, 6) becomes (6, -2).
To rotate a point 180 degrees about the origin, make both coordinates negative: (4, 1) becomes (-4, -1). For a 90 degree clockwise rotation, swap the coordinates and make the new second one negative: (1, 3) becomes (3, -1).
After any transformation, check one side length or angle on the image against the original. If they match, the shape stayed congruent and you did the move correctly.
Reflections, rotations, and translations move a shape to a new position without changing its size or angles.
Watch it
Where it sits
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.