---
title: "LACS.GSR.5: Matrices as geometric transformations (Georgia Mathematics standard)"
code: LACS.GSR.5
cite_as: Georgia Standards of Excellence, Mathematics, LACS.GSR.5
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/LACS.GSR.5
md_url: https://georgiahomeroom.org/standards/code/LACS.GSR.5.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/LACS.GSR.5.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# LACS.GSR.5: Matrices as geometric transformations

Solve contextual, mathematical problems involving matrices as geometric transformations and to explain real-life phenomena.

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## Expectations

- Find and use matrices which represent geometric transformations.
  - **LACS.GSR.5.1**: Given a 2-by-2 or 3-by-3 linear transformation matrix, describe the transformation a geometric figure undergoes.
  - **LACS.GSR.5.2**: Find matrices that represent scalings, reflections, and rotations of geometric figures.
  - **LACS.GSR.5.3**: Find a matrix that represents a combination of transformations.
  - **LACS.GSR.5.4**: Find the image of a point under a transformation.
  - **LACS.GSR.5.5**: Find the area of a polygon given its coordinates using matrices; find the area of the image of a polygon after a transformation.
  - **LACS.GSR.5.6**: Write code to perform transformations in two-dimensional geometry using matrix operations.
- Use matrices as functions.
  - **LACS.GSR.5.7**: Define functions from *n* dimensions to m dimensions as vectors and/or matrices.
  - **LACS.GSR.5.8**: Find the image and preimage of a linear map using matrices; determine whether the linear map is one-to-one.
  - **LACS.GSR.5.9**: Find and interpret geometrically the set of preimages of a vector under a given matrix.

## Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.