Course: 6.14 认识到翻译转变

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确认翻译转变
Have you ever seen an image like this? This diagram represents a transformation. Do you know which one?
::你见过这样的图象吗?这个图代表一个转变。你知道哪个图象吗?

In this concept, you will learn to recognize translation transformations.
::在此概念中,您将学会识别翻译转换。

Translation
::笔译笔译

A transformation is the movement of a geometric figure on the coordinate plane . There are several different types of transformations. One of these is called a translation. A translation is when a geometric figure slides up, down, left or right on the coordinate plane. The figure moves its location, but doesn’t change its orientation. It also doesn’t change its size or shape.
::转换是坐标平面上几何图的移动。有几种不同的转换类型。其中之一是翻译。翻译是几何图在坐标平面上向上、向下、向左或向右滑动。该图移动了位置,但没有改变方向。该图也不改变其大小或形状。

When you perform translations, you slide a figure left or right, up or down. This means that, in the coordinate plane, the coordinates for the vertices of the figure will change.
::当您执行翻译时,您会向上或向下向左滑动一个图。这意味着,在坐标平面中,图顶的坐标将发生变化。

You can represent this triangle by using coordinate notation . Coordinate notation is when you write ordered pairs to represent each of the vertices of a geometric figure that has been graphed on the coordinate plane.
::您可以使用坐标标记来代表此三角形。坐标标记是指您在坐标平面上绘制的几何图的每个顶点上写有顺序的对子时。

$\begin{align*}\begin{array}{rcl} (-1, 5) \\ (-1, 2) \\ (-5, 2) \end{array}\end{align*}$

These are the coordinates of the vertices of the triangle.
::这些是三角形顶端的坐标。

If you slide this triangle 3 places down, all of its vertices will shift 3 places down the $\begin{align*}y\end{align*}$ -axis. That means that the ordered pairs for the new vertices will change. Specifically, the $\begin{align*}y\end{align*}$ -coordinate in each pair will decrease by 3.
::如果您将三角形 3 滑动到下方, 所有的顶部都会将 Y 轴下方的 3 位移。这意味着新顶端的定购配对将会改变。具体地说, 每对的 Y 坐标将会减少 3 。

Now the $\begin{align*}y\end{align*}$ -coordinate of each ordered pair decreased by three units. You can see how the ordered pairs changed from the first image to the next image.
::现在,每对定购的Y座标减少了三个单位。您可以看到定购的一对是如何从第一个图像变成下一个图像的。

$\begin{align*}\begin{array}{rcl} (-1, 5) & \rightarrow \quad \ \ (-1, 2) \\ (-1, 2) & \rightarrow \quad (-1, -1) \\ (-5, 2) & \rightarrow \ \quad (-5, -1) \end{array}\end{align*}$

The $\begin{align*}y\end{align*}$ -coordinate changed from 5 to 2, from -1 to 2 and from 2 to -1. As you move down, the value of the coordinate also moved down. Similarly, if you were to move the image up three units on the $\begin{align*}y\end{align*}$ -axis, then you would increase the value of the $\begin{align*}y\end{align*}$ -coordinate by three units. Also if you were to move the image to the right then you would increase the $\begin{align*}x\end{align*}$ -coordinate. If you were to move it to the left, then you would decrease the $\begin{align*}x\end{align*}$ -coordinate.
::Y 坐标由 5 到 2 从 - 1 到 2 和 2 到 - 1 。当您向下移动时, 坐标值也向下移动。同样, 如果您将图像向 Y 轴上移动三个单位, 那么Y 坐标值会增加三个单位。另外, 如果您将图像向右移动, 您会增加 X 坐标。如果您向左移动, 那么会降低 X 坐标。

You can translate figures in other ways too. You can move figures diagonally by changing both their $\begin{align*}x\end{align*}$ - and $\begin{align*}y\end{align*}$ -coordinates. One way to recognize translations, then, is to compare their points. The $\begin{align*}x\end{align*}$ -coordinates will all change the same way, and the $\begin{align*}y\end{align*}$ -coordinates will all change the same way. To graph a translation, you perform the same change for each point .
::您也可以以其他方式翻译数字。您可以通过修改数字的 X 和 Y 坐标来将数字对角移动。那么,识别翻译的一个方法是比较它们的点。x 坐标将都以同样的方式变化,Y 坐标也将以同样的方式变化。要绘制翻译图,您对每个点都执行相同的变化。

Now let’s try graphing a translation. Take a look at this one.
::现在让我们试着绘制翻译的图表。看看这个。

Graph the following translation five places to the right.
::右侧5 位的翻译图。

First, you can see by looking at this square that there are four vertices, so there are four sets of ordered pairs to represent these vertices. List the ordered pairs.
::首先,你看这个方形可以看到有四个顶端, 所以有四组有顺序的对子代表这些顶端。列出有顺序的对子。

$\begin{align*}\begin{array}{rcl} (-4, 3) \\ (-1, 3) \\ (-1, 6) \\ (-4, 6) \end{array}\end{align*}$

Next, the translation is to move the square five places to the right. That means that you are going to change the $\begin{align*}x\end{align*}$ -coordinate and not the $\begin{align*}y\end{align*}$ -coordinate. List the new ordered pairs.
::接下来的翻译是将方形 5 位移到右边。这意味着您要更改 x 坐标, 而不是 Y 坐标。请列出新订购的对。

$\begin{aligned} \begin{array}{rcl} (- 4 + 5, 3) & = & (1, 3) \\ (- 1 + 5, 3) & = & (4, 3) \\ (- 1 + 5, 6) & = & (4, 6) \\ (- 4 + 5, 6) & = & (1, 6) \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} (-4 + 5, 3) &=& (1, 3) \\ (-1 + 5, 3) &=& (4, 3) \\ (-1 + 5, 6) &=& (4, 6) \\ (-4 + 5 ,6) &=& (1, 6) \end{array}\end{align*}$

Then, let’s look at the graph of the translation.
::那么,让我们看看翻译的图表。

This is the answer.
::这就是答案。

Notice that while it is helpful to graph the square both first and then as a translation, it isn’t necessary to do so to figure out the coordinate notation. If you know the vertices of the figure that you are translating and you know how you are moving it, then you can figure out the new coordinates of the vertices.
::请注意, 虽然先绘制正方形图然后作为翻译, 是有帮助的, 但无需找到坐标符号。如果您知道正在翻译的数字的顶点, 并且知道如何移动, 那么您就可以找到顶点的新坐标。

Examples
::实例

Example 1
::例1

Looking at this diagram, you can see that the figure, a quadrilateral has been shifted to the right and then up. It has not been flipped or turned. It has been moved, so this is a slide. Another name for a slide is a translation.
::查看此图表时, 您可以看到图中的数字, 一个四边形已经向右移动, 然后向上移动。它没有被翻转或翻转。它已被移动, 所以这是一张幻灯片。幻灯片的另一个名称是翻译。

The answer is that this transformation is a slide.
::答案是,这种转换是一个幻灯片。

Example 2
::例2

A triangle with the coordinates (0, 2), (2, 2) and (2, 5) is graphed on the coordinate grid. Find the coordinates of a translation moved three units down. Then graph the translation.
::坐标( 0, 2) 、 2, 2 和 2, 5) 的三角形在坐标网格上图解。查找翻译将三个单位移到下方的坐标。然后绘制翻译图解。

First, notice the direction of the translation. It is to move the triangle three units down. Down means that you will be subtracting three and down also means that you will be changing the $\begin{align*}y\end{align*}$ -coordinate since up and down involves the $\begin{align*}y\end{align*}$ -axis. List the ordered pairs for the translated triangle.
::首先,注意翻译的方向。它要将三角形的3个单位向下移动。向下意味着您将减去3个单位和向下, 也意味着您将更改 Y 坐标, 因为从上到下涉及到 Y 轴。列出翻译三角形的定购对。

$\begin{aligned} \begin{array}{rcl} (0, 2 - 3) & = & (0, - 1) \\ (2, 2 - 3) & = & (2, - 1) \\ (2, 5 - 3) & = & (2, 2) \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} (0, 2-3) &=& (0, -1) \\ (2, 2-3) &=& (2, -1) \\ (2, 5-3) &=& (2, 2) \end{array}\end{align*}$

Next, graph the translation.
::下一位, 绘制翻译图。

This is the answer.
::这就是答案。

Use this diagram to answer the following questions.
::使用此图表回答下列问题。

Example 3
::例3

Is this figure a translation?
::这是翻译吗?

Look at $\begin{align*}\triangle IRT\end{align*}$ and $\begin{align*}\triangle I^{\prime} R^{\prime} T^{\prime}\end{align*}$ . What is happening to the triangles?
::看看这些三角形是怎么回事?

The vertices of $\begin{align*}\triangle IRT\end{align*}$ have moved to the right 6 units and down 4 units. $\begin{align*}\triangle I^{\prime} R^{\prime} T^{\prime}\end{align*}$ is the translation of $\begin{align*}\triangle IRT\end{align*}$ .
::“IRT”的顶端已移到右侧的 6 个单位, 向下移到 4 个单位。“I`R'T ” 是“IRT”的翻译。

The answer is that yes, this is a translation. Remember a translation is a transformation that is informally called a slide or a glide.
::答案是是是, 这是翻译。记住, 翻译是一个转换, 非正式地称为幻灯片或滑翔。

Example 4
::例4

How many units up or down has the figure been moved?
::数字上下移动了多少个单位?

First, look at the vertices in the triangles to compare.
::首先,看看三角形中的顶峰来比较。

Point $\begin{align*}I\end{align*}$ has coordinates (-2, 8) and Point $\begin{align*}I^{\prime}\end{align*}$ has coordinates (4, 4). All other vertices change in the same way.
::I点有坐标(-2、8)和I`点有坐标(4、4)。所有其他的顶点都以同样方式变化。

Next, look at the change in the coordinates. Asking if the figure means up or down is the same as asking what the change in the $\begin{align*}y\end{align*}$ -coordinate is
::下一步,请看看坐标的改变。询问数字的上下含义是否与询问 Y 坐标的改变是什么相同。

$\begin{aligned} 8 - 4 = 4 \end{aligned}$
$\begin{align*}8 \ {\color{red}- \ 4} = 4\\\end{align*}$

The answer is that the figure moves 4 units down or -4.
::答案是,这个数字将4个单位向下移动或4个单位。

Example 5
::例5

How many units to the right or left?
::右边或左边有多少单位?

First, look at the vertices in the triangles to compare.
::首先,看看三角形中的顶峰来比较。

Point $\begin{align*}I\end{align*}$ has coordinates (-2, 8) and Point $\begin{align*}I^{\prime}\end{align*}$ has coordinates (4, 4). All other vertices change in the same way.
::I点有坐标(-2、8)和I`点有坐标(4、4)。所有其他的顶点都以同样方式变化。

Next, look at the change in the coordinates. Asking if the figure means left or right is the same as asking what the change in the $\begin{align*}x\end{align*}$ -coordinate is
::下一步,请看看坐标的更改。询问图的左或右意是否与询问 X 坐标的更改相同。

$\begin{aligned} - 2 + 6 = 4 \end{aligned}$
$\begin{align*}-2 \ {\color{red}+ \ 6} = 4\end{align*}$

The answer is that the figure moves 6 units to the right or +6.
::答案是图向右移动6个单位或+6。

Review
::回顾

Use the following diagram to answer each question.
::使用下图回答每个问题。

1. What kind of transformation is shown in the diagram?
::1. 图中显示何种变异?

2. What are the coordinates of the original blue triangle?
::2. 原始蓝色三角形的坐标是多少?

3. What are the coordinates of the translated red triangle?
::3. 红色三角形翻译的坐标是什么?

4. What direction was the triangle first moved?
::4. 三角形最初移动的方向是什么?

5. By how many units horizontally?
::5. 横向多少单位?

6. In what vertical direction was the triangle translated?
::6. 三角形的垂直方向是什么?

7. By how many units vertically?
::7. 垂直多少单位?

8. What are the coordinates of the original blue triangle?
::8. 原始蓝色三角形的坐标是多少?

9. What are the coordinates of the translated red triangle?
::9. 红色三角形翻译的坐标是什么?

10. In what horizontal direction was the triangle translated?
::10. 三角形的横向方向是什么?

11. By how many units horizontally?
::11. 横向多少单位?

12. In what vertical direction was the triangle translated?
::12. 三角形的垂直方向是什么?

13. By how many units vertically?
::13. 垂直多少单位?

14. True or false. Another name for a slide is a translation.
::14. 真实的或假的,幻灯片的另一个名称是译文。

15. True or false. A rotation and a translation have the same characteristics.
::15. 真实的或虚假的,旋转和翻译具有相同的特点。

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

Section outline

General

确认翻译转变

Translation ::笔译 笔译

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Translation
::笔译笔译

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源