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Transformations on the Coordinate Plane

  • Grade 8
  • Mathematics
  • 8.G.A.3
  • Geometry
  • Free lesson

Aligned to 8.G.A.3 — Common Core State Standards for Mathematics.

What this lesson teaches

Using coordinates: a translation adds to x or y; a reflection across an axis changes a sign; a rotation about the origin swaps and/or negates coordinates; and a dilation multiplies each coordinate by a scale factor k, changing the size.

Worked examples

Example 1

Dilate point (2, 3) by scale factor k = 3 about the origin by multiplying each coordinate by 3, giving (6, 9). The point moves 3 times farther from the origin, so the figure grows 3 times larger.

Example 2

Dilate (8, −4) by k = 1/2 about the origin: multiply each coordinate by 1/2 to get (4, −2). A factor under 1 shrinks the figure.

Example 3

Apply transformations in order. Reflecting then translating usually lands somewhere different from translating then reflecting.

Practice questions

  1. Dilate (4, −2) by a scale factor of 2 about the origin.
  2. Reflect (−3, 5) across the y-axis.
  3. A triangle is dilated by k = 1/2. How do its side lengths change?

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.

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En español

Transformaciones en el Plano Cartesiano

Usando coordenadas: una traslación suma a x o a y; una reflexión sobre un eje cambia un signo; una rotación alrededor del origen intercambia o niega coordenadas; y una dilatación multiplica cada coordenada por un factor de escala k, cambiando el tamaño.

Ejemplo 1: Dilata el punto (2, 3) por un factor de escala k = 3 alrededor del origen multiplicando cada coordenada por 3, lo que da (6, 9). El punto se aleja 3 veces más del origen, así que la figura crece 3 veces más grande.

Ejemplo 2: Dilata (8, −4) por k = 1/2 alrededor del origen: multiplica cada coordenada por 1/2 para obtener (4, −2). Un factor menor que 1 encoge la figura.

Ejemplo 3: Aplica las transformaciones en orden. Reflejar y luego trasladar suele caer en un lugar distinto que trasladar y luego reflejar.

More Geometry lessons

The Pythagorean Theorem8.G.B.7Properties of Transformations8.G.A.1Congruence Through Transformations8.G.A.2Similarity Through Dilations8.G.A.4Angle Relationships8.G.A.5The Pythagorean Theorem8.G.B.6

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