Understanding Translations in Mathematics: Moving Figures without Changing Shape or Size

Translation

Translation is a concept in mathematics that involves moving a figure or object from one location to another without changing its shape or size

Translation is a concept in mathematics that involves moving a figure or object from one location to another without changing its shape or size. This movement can be done by sliding, flipping, or rotating the original figure. The translated figure will have the same angles, lengths, and overall shape as the original, but it will be in a different location on the coordinate plane.

To perform a translation, you will need to know the magnitude and direction of the translation. The magnitude refers to the distance and direction refers to the path which the figure moves. Often, translations are described using vector notation.

Here’s an example of how to perform a translation:

Let’s say we have a triangle with vertices at points A(1, 2), B(3, 4), and C(5, 6). We want to translate this triangle 3 units to the right and 2 units up.

To perform the translation, we will add the magnitude of the translation to the current coordinates of each point. In this case, we add 3 to the x-coordinates and 2 to the y-coordinates. So, the new coordinates of the translated triangle would be:

A'(1 + 3, 2 + 2) = A'(4, 4)
B'(3 + 3, 4 + 2) = B'(6, 6)
C'(5 + 3, 6 + 2) = C'(8, 8)

Now, if you plot these new coordinates, you will see that the triangle has been translated 3 units to the right and 2 units up, while maintaining its original shape and size.

It is important to note that translations can also be done on larger shapes, such as polygons or even on complex figures. The same principle applies: you add the magnitude of the translation to each coordinate of the object to move it to the desired location.

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