Transformations as Functions
Aligned to G-CO.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
A transformation is a rule (a function) that assigns each point in the plane to an image point. Rigid motions (translations, rotations, reflections) preserve distance and angle, so the image is the same size and shape. Non-rigid transformations, like a dilation with scale factor not equal to 1, change distances.
Worked example
The translation (x, y) -> (x + 3, y - 2) is a function on points. Apply it to A(1, 4): image is (1 + 3, 4 - 2) = (4, 2). Apply it to B(1, 1): image is (4, -1). Distance AB was 3; distance between images is also 3, so distance is preserved — it is a rigid motion.
Practice questions
- Apply the rule (x, y) -> (x - 5, y + 1) to the point (2, 3).
- The rule (x, y) -> (2x, 2y) doubles coordinates. Show it is NOT a rigid motion by comparing the distance from (0,0) to (1,0) before and after.
- Is a reflection a rigid motion? State what it preserves.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Transformaciones como funciones
Una transformación es una regla (una función) que asigna a cada punto del plano un punto imagen. Los movimientos rígidos (traslaciones, rotaciones, reflexiones) conservan la distancia y el ángulo, así que la imagen tiene el mismo tamaño y forma. Las transformaciones no rígidas, como una dilatación con factor de escala distinto de 1, cambian las distancias.
Ejemplo: La traslación (x, y) -> (x + 3, y - 2) es una función sobre puntos. Aplícala a A(1, 4): la imagen es (1 + 3, 4 - 2) = (4, 2). Aplícala a B(1, 1): la imagen es (4, -1). La distancia AB era 3; la distancia entre las imágenes también es 3, así que se conserva la distancia — es un movimiento rígido.
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