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  • 硬硬变换

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    Melvin is an artist. He enjoys drawing translations, reflections and rotations of shapes. He took a picture of a water lily and he has decided that he is going to change the picture when he does the painting. He wants to paint the water lily 6 inches to the right. If the pictures are held next to each other, what type of transformation will his painting appear to be?
    ::Melvin是一位艺术家。他喜欢绘画翻译、反射和形状的旋转。他拍摄了一幅水百合的照片,他决定当他画画的时候,他要改变画像。他想把水的利里6英寸画在右边。如果照片是相邻拍摄的,那么他的画会是什么类型的变形呢?

    In this concept, you will learn about transformations.
    ::在这个概念中,你会了解变革。

    Transformations
    ::变换

    A transformation is the movement of a geometric figure. There are three different kinds of transformations. 
    ::变换是几何数字的移动。 有三种不同的变换。

    In any transformation, the size and shape of the figure stay exactly the same, only its location changes or shifts.
    ::在任何变化中,数字的大小和形状保持不变,只有其位置变化或变化。

    The first type of transformation is called a translation . It is also known as a slide because the figure in question does exactly that. It moves up, down, to the left or to the right. Nothing about the figure changes except its location.
    ::第一种变换类型被称为翻译。它也被称为幻灯片,因为有关数字就是如此。它向上、向下、向左或向右移动。图中除了位置外没有任何变化。

    Here are a few examples of translations.
    ::以下是一些翻译的例子。

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    Notice when you look at each picture that all that changed for each figure is its location. There are different colors used to show you the actual translation, but other than the location, each looks exactly the same.
    ::当您看到每张图片时, 注意每张图中的所有变化都是它的位置。 使用不同的颜色来显示您实际的翻译, 但除了位置以外, 每个图像看起来都完全一样 。

    This is how you always know that you are working with a translation or a slide.
    ::这就是你总是知道 你的工作与翻译或幻灯片。

    To perform a translation, measure a distance then redraw the figure. For example, let’s move this triangle 6 inches.
    ::要进行翻译, 请测量距离, 然后重新绘制图。 例如, 让我们移动三角形 6 英寸 。

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    Measure 6 inches from each point of the triangle and make a new point. This way, every part of the triangle moves 6 inches.
    ::从三角形的每个点测量 6 英寸, 并设定一个新点。 这样, 三角形的每个部分都会移动 6 英寸 。

    The second type of transformation is a reflection . In a reflection, the figure flips to make a mirror image of itself. Take a look at the reflection below.
    ::第二种转型是反射。在反射中,图形翻转以形成反射图像。看看下面的反射。

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    The line in the middle acts like a mirror. This is the line of symmetry . When reflected, the figure above looks like a backwards L . Notice that, on both sides of the line, the dot is closest to the line.
    ::中间线的线像镜子一样。 这是对称线 。 如果反映的话, 上面的数字看起来像一个倒着的 L. 注意, 在线的两边, 点与线最接近 。

    You can also reflect figures across a horizontal line of symmetry. The reflection would look like this.
    ::您也可以在对称水平线上反射数字。反射会像这样。

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    In this case, the “top” of the figure becomes the “bottom” in the reflection. Notice, however, that in both cases the figures are symmetrical.
    ::在这种情况下,数字的“顶部”成为反射中的“底部”,但通知说,在这两种情况下,数字都是对称的。

    The third type of transformation is a rotation . A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.
    ::第三种变换类型是旋转。旋转类型是将数字转换成时钟或反时钟方向的转换。

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    Imagine you could spin the figure around in a circle . It would not change, but might turn upside down. Figures can rotate as much as 360 ∘ . Let’s see how that might look.
    ::想象一下,你可以将数字旋转在一个圆圈里。它不会改变,但可能会反转。数字可以旋转到360。让我们看看情况会如何。

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    When you rotate the figure a full 360 ∘ , it ends up in the same place it began.
    ::当您旋转一个完整的360时,它最终会位于它开始的位置。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Melvin and his painting.
    ::早些时候,有人给你一个问题 关于梅尔文和他的画。

    He wants to paint the water lily 6 inches to the right, which slides the original image. If the pictures are held next to each other, what type of transformation will his painting appear to be?
    ::他想将水的利里6英寸画到右边,这样可以滑动原始图像。如果照片是放在对方旁边,那么他的画会是什么类型的变形呢?

    First, reference the original image to see how the shape moved.
    ::首先,引用原始图像来查看形状是如何移动的 。

    The shape appears to have slid to the right.
    ::形状似乎滑到了右边。

    Next, review the different type of transformations.
    ::接下来,审查不同的变换类型。

    Translation, reflection, rotation.
    ::翻译,反射,轮换。

    Then, determine the type of transformation that slides a figure.
    ::然后,决定一个数字的变换类型。

    Translation.
    ::翻译。

    Example 2
    ::例2

    Solve the following problem.
    ::解决以下问题。

    If the figure is turned 90 o , what type of transformation will that be?
    ::如果数字是90o,那会是什么类型的转变?

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    First, note the description of the movement.
    ::首先,请注意该运动的描述。

    The figure is turned 90 o .
    ::数字是90o。

    Next, review the different types of transformations.
    ::接下来,审查不同类型的变换。

    Translation, reflection, rotation.
    ::翻译,反射,轮换。

    Then, determine the type of transformation that turns a figure.
    ::然后,决定一个数字的转换类型。

    Rotation.
    ::轮调。

    The answer is that it is a rotation.
    ::答案是,这是一个轮换。

    Example 3
    ::例3

    Name the transformation.
    ::命名变换 。

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    First, reference the dots to see how the shape moved.
    ::首先,引用点来观察形状是如何移动的。

    The shape appears to have flipped over a vertical line.
    ::形状似乎已经翻转到垂直线上 。

    Next, review the different type of transformations.
    ::接下来,审查不同的变换类型。

    Translation, reflection, rotation.
    ::翻译,反射,轮换。

    Then, determine the type of transformation that flips a figure.
    ::然后,确定翻转数字的转换类型。

    Reflection.
    ::反省。

    The answer is that it is a reflection.
    ::答案是,这是一个反思。

    Example 4
    ::例4

    What type of transformation has a line of symmetry?
    ::哪种变异有对称线?

    First, review the different types of transformation.
    ::首先,审查不同类型的转变。

    Translation, reflection, rotation.
    ::翻译,反射,轮换。

    Next, list what each transformation does.
    ::接下来,列出每个变换都做什么。

    Slide, flip, turn.
    ::滑动,翻转,转弯。

    Then, determine the type of transformation that flips over a line of symmetry.
    ::然后,确定在对称线上翻转的转换类型。

    Reflection.
    ::反省。

    Example 5
    ::例5

    Identify the transformation shown below as a translation, reflection, or rotation.
    ::标明下列转换为翻译、反思或轮换。

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    First, reference the dots to see how the shape moved.
    ::首先,引用点来观察形状是如何移动的。

    The shape appears to have turned.
    ::形状似乎变了

    Next, review the different type of transformations.
    ::接下来,审查不同的变换类型。

    Translation, reflection, rotation.
    ::翻译,反射,轮换。

    Then, determine the type of transformation that turns a figure.
    ::然后,决定一个数字的转换类型。

    Rotation.
    ::轮调。

    Review
    ::回顾

    Identify the transformations shown below as translations, reflections, or rotations.
    ::标明下列翻译、反思或轮换的变换。

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    Tell whether the figures below have line symmetry, rotational symmetry, both, or neither.
    ::说明下图是否具有线对称、旋转对称,或两者兼有。

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    Draw the second half of each figure.
    ::绘制每个图的后半部分。

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    Review (Answers)
    ::回顾(答复)

    Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
    ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

    Resources
    ::资源