Properties of Transformations
Aligned to 8.G.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
Rotations, reflections, and translations are rigid motions: they preserve lengths and angle measures. Lines map to lines, segments to segments of the same length, and angles keep the same measure.
Worked example
Translate segment AB with A(1, 2) and B(4, 2) right 3 and up 1 by adding (3, 1) to each point: A'(4, 3), B'(7, 3). The length stays 4 − 1 = 3 units for AB and 7 − 4 = 3 for A'B', showing length is preserved.
Practice questions
- Reflect the point (5, 3) across the x-axis.
- Translate the point (−2, 4) left 5 and down 2.
- Explain why a 90° rotation does not change the length of a segment.
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
Propiedades de las Transformaciones
Las rotaciones, reflexiones y traslaciones son movimientos rígidos: conservan las longitudes y las medidas de los ángulos. Las rectas se transforman en rectas, los segmentos en segmentos de la misma longitud y los ángulos conservan su medida.
Ejemplo: Traslada el segmento AB con A(1, 2) y B(4, 2) 3 a la derecha y 1 hacia arriba sumando (3, 1) a cada punto: A'(4, 3), B'(7, 3). La longitud sigue siendo 4 − 1 = 3 unidades para AB y 7 − 4 = 3 para A'B', lo que muestra que la longitud se conserva.
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