In geometry, a translation means moving an object to the left, right, upwards, or downwards without rotating, resizing, or anything else.
Let's take a look at the two triangles and shown below.
A few things to note:
The original shape, is called the preimage. The shape the result of the translation, is called the image. In our case, the preimage has been translated units to the right and units upward.
It's important to realize that every point on is translated to a point on The diagram shows the triangle's vertices being translated, but the same translation applies to every point on each side of the triangle as well.
A translation is a type of transformation. There are other types of transformations that we'll learn more about later.
The triangle (shown below) is shifted units to the right and units downward to give the triangle Plot the resulting triangle.
First, we must translate each point of the triangle units to the right. To accomplish this, we can translate each vertex units to the right and then draw in the line segments between the new vertices.
Next, we must translate each point of the resulting triangle units downward. Again, we translate the vertices and then draw in the line segments between the new vertices. The diagram below shows the resulting triangle.
Which of the following statements is true regarding the figures $\mathcal{P}$ and $\mathcal{Q}$ shown above?
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a
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$\mathcal{Q}$ is the result of the translation of $\mathcal{P}$ by $4$ units to the left and $3$ units downward |
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b
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$\mathcal{Q}$ can't be obtained from $\mathcal{P}$ using only a translation |
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c
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$\mathcal{Q}$ is the result of the translation of $\mathcal{P}$ by $3$ units to the left |
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d
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$\mathcal{Q}$ is the result of the translation of $\mathcal{P}$ by $4$ units downward |
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e
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$\mathcal{Q}$ is the result of the translation of $\mathcal{P}$ by $3$ units to the left and $4$ units downward |
The polygon $\mathcal{P}$ (shown above) is shifted $3$ units to the right and $5$ units upward to give the polygon $\mathcal{Q}.$ Which of the following diagrams correctly represents the given situation?
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b
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c
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Consider the transformation that translates the point by units to the right and units up, as shown below.
We can express this transformation by writing it as a function, as follows:
The function above takes a point as its input and gives another point as output. Let's check it with our point
Any translation of units to the right and units up can be written using any of the following notations:
If is negative, then the function translates the point by units to the left. If is negative, then the function translates the point by units downwards.
The triangle shown below is translated using the function Plot the resulting triangle.
The translation is a shift by units to the right and units downward.
First, we must translate each point unit to the right. To accomplish this, we can translate each vertex units to the right and then draw in the line segments between the new vertices.
Next, we must translate each point of the resulting figure units downward. Again, we translate the vertices and then draw in the line segments between the new vertices. The diagram below shows the resulting triangle.
The line segment shown above is translated using the function $T(x,y) = (x+3, y+5).$ What is the resulting segment?
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The triangle shown above is translated using the function $f(x,y) = (x-1,y+5).$ What is the resulting triangle?
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The translation maps the polygon to the polygon as shown above. What are the values of and
Every point belonging to is translated in the same way. Therefore to determine the values of and we can consider any point of the polygon.
Let's consider the vertex Under the translation, it moves to So, we have
We establish the values of and by considering the - and -coordinates of the above transformation.
Looking at the -coordinates, we must have so
Looking at the -coordinates, we must have so
Therefore, and
The translation $T$ given by the function $f(x,y) = (x+p, y+q)$ maps the triangle $\mathcal{P}$ to the triangle $\mathcal{Q},$ as shown above. What are the values of $p$ and $q?$
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a
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$p=-4$ and $q=4$ |
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b
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$p=4$ and $q=6$ |
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c
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$p=4$ and $q=-4$ |
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d
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$p=-4$ and $q=-4$ |
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e
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$p=6$ and $q=4$ |
The translation $T$ given by the function $(x,y) \mapsto (x+p, y+q)$ maps the point $(-15,5 )$ to the point $(1, 7).$ What are the values of $p$ and $q?$
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a
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$p=-14$ and $q=2$ |
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b
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$p=-8$ and $q=12$ |
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c
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$p=16$ and $q=2$ |
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d
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$p=-14$ and $q=-2$ |
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$p=-16$ and $q=12$ |
A translation maps the polygon to the polygon as shown above. What is the functional representation of
Note that if we translate the polygon by units to the right and units upward, then we get the polygon
Therefore, the functional representation of the transformation is
A translation $T$ maps the polygon $\mathcal P$ to the polygon $\mathcal Q,$ as shown above. What is the functional representation of $T?$
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a
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$T(x,y) = (x+4,y-6)$ |
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b
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$T(x,y) = (x-6,y+4)$ |
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c
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$T(x,y) = (x+4,y+6)$ |
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d
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$T(x,y) = (x+6,y+4)$ |
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e
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$T(x,y) = (x+6,y-4)$ |
A translation $f$ maps the polygon $\mathcal P$ to the polygon $\mathcal Q,$ as shown above. What is the functional representation of $f?$
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a
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$f(x,y)= (x-4,y+2)$ |
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b
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$f(x,y)= (x+4,y-2)$ |
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c
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$f(x,y)= (x-4,y-2)$ |
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d
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$f(x,y)= (x+4,y+2)$ |
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e
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$f(x,y)= (x-2,y-4)$ |