YourHomeschool YourHomeschool Curriculum By state Workbooks Games Open the Tutor
Curriculum › Grade 8 › Mathematics

Properties of Transformations

  • Grade 8
  • Mathematics
  • 8.G.A.1
  • Geometry
  • Free lesson

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 examples

Example 1

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.

Example 2

Reflect A(3, 5) across the x-axis: the y-coordinate flips sign, giving A'(3, −5). Distances are unchanged.

Example 3

Rotations, reflections and translations preserve size and shape; only a dilation changes size. That is why the first three produce congruent figures and a dilation produces a similar one.

Practice questions

  1. Reflect the point (5, 3) across the x-axis.
  2. Translate the point (−2, 4) left 5 and down 2.
  3. 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 lesson

En 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 1: 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.

Ejemplo 2: Refleja A(3, 5) sobre el eje x: la coordenada y cambia de signo, dando A'(3, −5). Las distancias no cambian.

Ejemplo 3: Las rotaciones, reflexiones y traslaciones conservan tamaño y forma; solo la dilatación cambia el tamaño. Por eso las primeras tres producen figuras congruentes y la dilatación una semejante.

More Geometry lessons

The Pythagorean Theorem8.G.B.7Congruence Through Transformations8.G.A.2Transformations on the Coordinate Plane8.G.A.3Similarity Through Dilations8.G.A.4Angle Relationships8.G.A.5The Pythagorean Theorem8.G.B.6

Teach this lesson today

An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.

Start free — no card required