Translations of Lines

After this lesson, you will be able to use a vector to translate a line, and visualize the possible results.

The lesson begins by teaching you to translate a line along a vector to create a parallel line. It leads you to learn to translate a line along a vector to create a line that coincides with the original. It concludes with the idea that, given a line and a point not on it, there is exactly one line through the point that is parallel to the original line.

Learn about translations and parallel lines by helping Akio become a zen garden master!

This video includes key concepts, notation, and vocabulary such as translation (moving a geometric object without changing its size or shape); vector (a directed line segment which shows us the length and direction of the translation); image (the object which results from the translation of an original); prime notation (if the original line is ‘L’, the image after translation is ‘L’’, that is, ‘L’ prime); parallel lines (two lines in a plane which don’t intersect); and coincident lines (two lines in a plane which intersect in all their points).

Before watching this video, you should already be familiar with the idea that translation is moving an object along a vector to create a new object that has the same size and shape; the idea that lines in a plane can be intersecting or parallel; and the idea that coincident lines overlap each other completely.

After watching this video, you will be prepared to learn how to transform lines and other objects using translation, rotation or reflection.

Common Core Standard(s) in focus: 8.G.A.1 A video intended for math students in the 8th grade Recommended for students who are 13 - 14 years old