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We can describe a transformation using words, symbols, or models.
See solution.
We are asked to explain how we can best show or describe the change in position of a figure after a transformation. In general, when considering a transformation, we can describe the change in position of a figure using words, symbols, or models. Let's consider each transformation separately.
A translation slides a figure from one position to another, without changing its shape or turning it. Let's consider an example figure.
Now let's think about a translation that moves our triangle 5 units left and 3 units down. First, we will describe it using words.
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The translation moves the figure 5 units left and 3 units down. |
A reflection results in a mirror image of the figure. There are two main types of reflections: over the x-axis and over the y-axis. Once again, we consider an example figure.
Let's describe both types of reflections using words.
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After a reflection over the x-axis, the y-coordinates of the points of the preimage are multiplied by - 1. |
Next, we can describe these two transformations using symbols. Reflection over thex-axis:& (x, y) →(x,- y) Reflection over they-axis:& (x, y) →(- x, y) Finally, we represent the reflections using models.
A rotation turns a figure about the center of rotation. Here, we will consider rotations where the center is the origin. Let's consider an example figure again.
We know 3 main types of clockwise rotations: by 90^(∘), by 180^(∘), and by 270^(∘). Let's describe each of these rotations using words.
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The triangle is rotated 90^(∘) clockwise about the origin. |
A dilation enlarges or reduces a figure. We will consider dilations where the center of dilation is the origin. Let's consider an example figure.
There are three types of dilations depending on the value of the scale factor k. Let's describe each of them using words.
| Dilation | |
|---|---|
| k > 1 | Enlargement: the image is bigger than the preimage. |
| 0 < k < 1 | Reduction: the image is smaller than the preimage. |
| k = 1 | The image is the same size as the preimage. |
