---
title: "Coordinate Transformations"
description: "Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original"
canonical: https://lightmysky.com/learn/mathematics/coordinate-transformations-mt_K0Y15w48SY
source: https://lightmysky.com/learn/mathematics/coordinate-transformations-mt_K0Y15w48SY.md
retrieved: 2026-10-19
---

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# Coordinate Transformations

Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original

Subject: Mathematics · Area: Geometry · Ages 11 to 14
Page: https://lightmysky.com/learn/mathematics/coordinate-transformations-mt_K0Y15w48SY

## Ready when they can

- Reflect a shape in a given mirror line (including diagonal lines) and state the coordinates of the image
- Rotate a shape about a given centre by 90 or 180 degrees and describe the result
- Translate a shape by a given vector and verify that lengths and angles are preserved
- Update both coordinates by the horizontal and vertical increments of a translation
- Reflect across x = c by keeping y and placing x the same distance on the other side

## Lesson: Reflecting, Rotating, and Translating on a Grid

You already know how to slide a shape and flip it on a grid. A rotation turns a shape around a fixed point. These moves do not stretch or squash a shape, so side lengths and angles stay the same.

*(drawing: A rigid move can slide, flip, or turn a triangle, but it keeps the same size and shape.)*

**Example.** To reflect a point in the diagonal line y = x, swap its two coordinates. Point (2, 5) becomes (5, 2).

**Example.** A 180 degree rotation about the origin changes (x, y) to (-x, -y). A 90 degree clockwise rotation changes (x, y) to (y, -x).

A translation changes coordinates by its movement. Moving right adds to x, moving left subtracts from x, moving up adds to y, and moving down subtracts from y. A reflection in x = c keeps y and places x the same distance on the other side.

A reflection in y = x swaps the coordinates. For example, (-6, 2) becomes (2, -6). The point has the same distance from the mirror line on each side.

For a 90 degree clockwise turn about the origin, swap coordinates and make the second coordinate negative. For example, (6, 2) becomes (2, -6). A half-turn changes both signs.

**Recap.** Reflections, rotations, and translations move a shape to a new position without changing its size or angles.

## Practice

18 questions on this page, each with its working shown.

## Needs first

- [Coordinates (age 11+)](https://lightmysky.com/learn/mathematics/coordinates-age-11-mt_hVpGOEz2kG)
- [Translating and reflecting shapes](https://lightmysky.com/learn/mathematics/translating-and-reflecting-shapes-mt_lxaM6iVpdr)

## Opens up

- [Vectors: Notation, Addition and Scalar Multiples](https://lightmysky.com/learn/mathematics/vectors-notation-addition-and-scalar-multiples-mt_NkqmrL7pLe)
- [Similarity and enlargement](https://lightmysky.com/learn/mathematics/similarity-and-enlargement-mt_y-BuQAfw4B)