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TRANSLATIONS |
| Geometry | |
| 1. TraNslaTiOn USING VECTORS | |
| A translation of vector V transforms point A into point A' so that vectors V and AA' are equivalent (or equipollent). Vectors BB' and CC' are also equivalent to V, which is why distances between corresponding points are the same. The triangle ABC in the Descartes window is transformed into A'B'C' with the translation of vector V, whose coordinates are V.x and V.y. Different translations of this triangle are obtained by changing the vector coordinates with the arrows. | |
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1.-
Look carefully at the set of axes and work out the coordinates of each
of the vertices of triangle ABC
as well as the coordinates of the corresponding vertices of triangle A'B'C'. Is there any relation between
these coordinates and those of the vector V? 2.- Draw triangle ABC and its transformation A'B'C' in your exercise book after each of the following translations: (-2,1), (3,-1), (5,2) y (5,-2). Check your results in the window when you have finished.
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| 2. THE VECTOR OF A TRANSLATION | |
| The following window shows a random translation of the blue triangle whose transformation is turquoise. We need to work out the coordinates of the vector which has been used to translate the triangle. | |
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| 3.- Click once on the Init button in the left-hand window and look carefully at both triangles. Copy them into your exercise book and try to work out the coordinates of the vector of the transformation. Check your results by using the right-hand window. If you are not correct find the answer by changing the vector coordinates until the turquoise triangle is in the same position as it is in the left-hand window. Repeat the exercise at least 10 times. | |
| 3. COMBINATIONS OF TRANSLATIONS | |
| Combining two translations of vectors U and V is the same as one translation of vector U+V. In the Descartes window we have drawn two random vector transformations, which as you can see, coincide with the vector which is the sum of both. | |
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| 4.-
Click
on the Init button in the window. Then, look carefully at each shape
and look at the translations that the blue triangle and turquoise
triangle undergo. Check that the sum of these two vectors is equal to
the sum vector. 5.- Carry out the following translations: U=(3,2) & V=(4,-6); U=(10,3) & V=(-3,-8); U=(-3,2) & V=(-4,-6). For the last example move the axes to the right (O.x=160). 6.- Check that the combination of translations is commutative, as it is the sum of the vectors. Click on the Init button and then draw the sum of vectors U=(4,3) & V=(3,-1). Draw both combinations into your exercise book and check that they are the same.
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| Miguel García Reyes | ||
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| Spanish Ministry of Education. Year 2001 | ||
Except where otherwise noted, this work is licensed under a Creative Common License