Mastering Translations in Mathematics: A Comprehensive Guide to Understanding and Performing Translations with Ease

Translation

Translation in mathematics refers to the process of moving or shifting a figure or shape from one position to another without changing its size, shape, or orientation

Translation in mathematics refers to the process of moving or shifting a figure or shape from one position to another without changing its size, shape, or orientation. It involves moving every point of the figure in the same direction and by the same distance.

To perform a translation, you need to know how much and in which direction the figure should be moved. This information is usually given as a set of coordinates or as a vector.

Here are the steps to perform a translation:

1. Identify the figure or shape that needs to be translated.
2. Determine the amount and direction of the translation by either reading the coordinates given or using the vector provided.
3. Move each point of the figure the same distance and direction as determined in the previous step.
4. Plot the new points to obtain the translated figure.

For example, let’s say we have a triangle with vertices A(2, 4), B(5, 6), and C(7, 3). We are asked to translate it 3 units to the right and 2 units down.

To perform the translation, we add the translation values to the x-coordinates and subtract them from the y-coordinates of each vertex:
A'(2 + 3, 4 – 2) = A'(5, 2)
B'(5 + 3, 6 – 2) = B'(8, 4)
C'(7 + 3, 3 – 2) = C'(10, 1)

Plotting the new points A'(5, 2), B'(8, 4), and C'(10, 1), we obtain a translated triangle.

It is important to note that translations involve moving the entire figure, so all distances and angles within the figure remain unchanged. Additionally, translations can be performed in any direction and by any distance, positive or negative.

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