Translation in Mathematics

Translation in mathematics refers to the process of moving a figure from one location to another without changing its size, shape, or orientation. This movement is typically described using coordinate notation, where the x and y coordinates of each point in the figure are shifted by a certain amount.

Translation Notation

In a two-dimensional coordinate system, the translation of a figure can be described using the following notation:

If a point has coordinates (x, y), and it is translated by (a, b), then the new coordinates of the point will be (x+a, y+b).

Example

For example, if we have a point A with coordinates (2, 3) and we want to translate it by (4, -1), the new coordinates of A will be (2+4, 3+(-1)) = (6, 2).

Study Guide for Translation

Understand the concept of translation: Moving a figure from one location to another without changing its size, shape, or orientation.
Learn the notation for translation: Understand how to describe the translation of a point using coordinate notation.
Practice translating figures: Practice translating points, lines, and shapes on a coordinate plane.
Understand the properties of translation: Recognize that translation preserves distance and angle measures.
Apply translation to real-world problems: Understand how translation can be used to describe the movement of objects in real-life situations.

By mastering the concept of translation and practicing the notation and properties, you will be able to confidently work with translations of geometric figures.

◂Math Worksheets and Study Guides Seventh Grade. Measurement, Perimeter, and Circumference

Study Guide

Measurement, Perimeter, and Circumference

Worksheet/Answer key

Measurement, Perimeter, and Circumference

Worksheet/Answer key

Measurement, Perimeter, and Circumference

Worksheet/Answer key

Measurement, Perimeter, and Circumference

The resources above cover the following skills:

Geometry (NCTM)

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Connections to the Grade 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.