Often in math class you will be asked to translate a figure, like a triangle or circle, down and up or left and right. A translation is a transformation that moves the figure to a new location in the coordinate plane, but it doesn’t change the shape of the figure or its size. The x and y coordinates of the vertices of the figure will change when you perform a translation. To graph a translation you will need to use ordered pairs to represent the vertices of the figure, and then you will need to shift each pair by the same amount, which will be equal to the magnitude of the translation.
For example, if the triangle is translated down five units, each x-coordinate will decrease by five and each y-coordinate will increase by three. This will give the new vertices of the triangle as shown below.
Sometimes you will be given a problem where the pre-image of a figure is reflected over the x-axis and then translated down, or mirrored. This can be a little confusing because the order of these transformations can change what the vertices of the final image will be. To help you solve this type of problem, it is important to learn how to recognize that a reflection and a translation are the same thing, so you can understand what is happening with the vertices of the figure.
If you were given the following problem, what would be the answer if figure x is translated down 5 and then reflected over the y-axis?
The image below shows the triangle before a reflection and after a translation. To get the new image of the triangle you must first reflect it over the y-axis. Then you must translate down 5 and up 7. This will give the image of the triangle as shown below. To get the new vertices of this triangle you must use ordered pairs to represent them, and then you must shift each pair by the same amount, which is equal to the magnitude of the translation.
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