--- title: "Translating and reflecting shapes" description: "Draw and translate simple shapes on the coordinate plane; reflect shapes in the axes" canonical: https://lightmysky.com/learn/mathematics/translating-and-reflecting-shapes-mt_lxaM6iVpdr source: https://lightmysky.com/learn/mathematics/translating-and-reflecting-shapes-mt_lxaM6iVpdr.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Translating and reflecting shapes Draw and translate simple shapes on the coordinate plane; reflect shapes in the axes Subject: Mathematics · Area: Geometry · Ages 10 to 11 Page: https://lightmysky.com/learn/mathematics/translating-and-reflecting-shapes-mt_lxaM6iVpdr ## Ready when they can - Translate a triangle 3 units right and 2 units down on a coordinate grid and state the new coordinates - Reflect a shape in the x-axis and list the coordinates of the reflected vertices - Explain how translation changes coordinates (add/subtract) while reflection changes the sign of one coordinate ## Lesson: Translating and Reflecting Shapes A translation slides a shape without turning it or flipping it. Every point on the shape moves the same distance in the same direction. On a coordinate grid, moving right or left changes the x-coordinate, and moving up or down changes the y-coordinate. **Example.** A triangle has corners at (1, 1), (4, 1), and (2, 3). Translate it 3 units right and 2 units down. Add 3 to every x-coordinate and subtract 2 from every y-coordinate. The new corners are (4, -1), (7, -1), and (5, 1). *(drawing: Watch one corner of the triangle. It slides 3 units right and 2 units down, so (1, 1) becomes (4, -1). Every other corner makes exactly the same slide.)* A reflection flips a shape across a line, like a mirror. Reflecting a shape in the x-axis keeps every x-coordinate the same but flips the sign of every y-coordinate. Reflecting in the y-axis works the other way: the y-coordinate stays the same, and the x-coordinate flips sign. A slide is different: it adds or subtracts the same amount from each coordinate instead of changing a sign. **Example.** A triangle has corners at (1, 2), (3, 2), and (2, 4). Reflect it in the x-axis. Keep each x-coordinate the same and flip the sign of each y-coordinate. The new corners are (1, -2), (3, -2), and (2, -4). **Tip.** Translating is a slide: add or subtract the same number from every point. Reflecting is a flip: only one coordinate changes sign, and the other stays exactly the same. **Recap.** Translating slides a shape by adding or subtracting the same amount from every coordinate; reflecting flips the sign of one coordinate while the other stays the same. ## Practice 13 questions on this page, each with its working shown. ## Needs first - [Reflection and Translation on a Grid](https://lightmysky.com/learn/mathematics/reflection-and-translation-on-a-grid-mt_efOeaGFyGM) - [Coordinates (age 10+)](https://lightmysky.com/learn/mathematics/coordinates-age-10-mt_R4AY0LKxfl) ## Opens up - [Coordinate Transformations](https://lightmysky.com/learn/mathematics/coordinate-transformations-mt_K0Y15w48SY)