Drawing and Sequencing Transformations
Aligned to G-CO.A.5 — Common Core State Standards for Mathematics.
What this lesson teaches
Given a figure and a transformation, you can draw the image point by point. Often two figures are related by a sequence of rigid motions rather than a single one. Finding that sequence proves the figures are congruent.
Worked example
Triangle with vertices A(1,1), B(4,1), C(1,3). Reflect it across the y-axis using (x, y) -> (-x, y). Image vertices: A'(-1,1), B'(-4,1), C'(-1,3). Plot the originals and images; the triangle flips to the left side, same size and shape. To then slide it up 2, follow with (x, y) -> (x, y + 2): A''(-1,3), B''(-4,3), C''(-1,5).
Practice questions
- Rotate the point (3, 0) by 90° about the origin using (x, y) -> (-y, x). Give the image.
- Reflect A(2, 5) across the x-axis, then translate the image right 4. Give the final coordinates.
- Describe a sequence of two rigid motions that carries a triangle onto its copy located 6 units to the right and flipped upside down.
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
Dibujar y encadenar transformaciones
Dada una figura y una transformación, puedes dibujar la imagen punto por punto. A menudo dos figuras se relacionan por una secuencia de movimientos rígidos en vez de uno solo. Encontrar esa secuencia demuestra que las figuras son congruentes.
Ejemplo: Triángulo con vértices A(1,1), B(4,1), C(1,3). Refléjalo sobre el eje y usando (x, y) -> (-x, y). Vértices imagen: A'(-1,1), B'(-4,1), C'(-1,3). Grafica los originales y las imágenes; el triángulo se voltea al lado izquierdo, del mismo tamaño y forma. Luego, para subirlo 2, aplica (x, y) -> (x, y + 2): A''(-1,3), B''(-4,3), C''(-1,5).
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