课程： 11.17整数转换，点之间的路径

章节大纲

选择节常规

折叠展开
常规

全部折叠展开全部
- 选择活动新闻通告
  
  新闻通告讨论区
选择节整数转换，点之间的路径

折叠展开
整数转换，点之间的路径
::[图1]

Reggie is taking art and has been given a picture of two people sitting in a room with a cat on the floor. His task is to redraw the picture but with the cat by the woman's feet, next to the sewing basket, instead of where it currently is. How can he figure out how to reorganize this image?
::雷吉正在拍摄艺术,并得到了两个人坐在一个房间里的图片。他的任务是重新画画,但用女人的脚和缝纫篮子旁边的猫来重新画画,而不是现在的缝纫篮子。他怎样才能想出如何重塑这幅图象呢?

In this concept, you will learn how to translate points from one place to another on a coordinate plane .
::在这个概念中,你将学会如何在协调飞机上将各点从一个地方翻译成另一个地方。

Translating Points on a Coordinate Plane
::坐标平面上的翻译点

A coordinate grid is a grid in which points are graphed. It usually has two or more intersecting lines which divide a plane into quadrants, and in which ordered pairs, or coordinates, are defined. It usually has four quadrants, or sections, to it.
::坐标网格是一个用图形绘制点数的网格。它通常有两个或两个以上的交叉线, 将平面分为四重方, 并定义定购的配对或座标。它通常有四个四重方, 或四分段。

The origin is the place where the two lines intersect. Its coordinates are defined as (0,0).
::来源是两条线交叉的地方。其坐标被定义为(0,0) 。

The x-axis is the line running from left to right that has the numbers defined on it and is usually labeled with an "x". The x-coordinate of an ordered pair is found with relation to it. All the points located on the x-axis have a y-coordinate of 0.
::X 轴是从左向右运行的线条,其编号是定义的,通常贴有“x”的标签。与该线条相关的是定购一对的X坐标。X 轴上的所有点都有0的Y坐标。

The y-axis is the central line that runs up-down and is labeled with a "y". Y-coordinates are plotted in reference to this axis. Again, all the x-coordinates of points located on the y-axis are 0.
::Y 轴是自上而下并贴有“y”标签的中心线。 Y 坐标是在此轴上绘制的。同样,Y 轴上的所有点的 X 坐标都是 0 。

An ordered pair is a list of two numbers in parenthesis, separated by a comma like this: (5,-3). It tells where a point is located on the coordinate plane. The first number is the x-coordinate. It tells you where to go on the x-axis. If it is positive, you go to the right. If it is negative, you go to the left. The second number is the y-coordinate. It tells you where to go on the y-axis. If it is positive, you go up. If it is negative, you go down.
::订购的一对是括号中两个数字的列表,用像这样的逗号分隔开来: (5, 3) 。它说明坐标平面上的点的位置。第一个数字是 x 坐标。它告诉您如何使用 x 轴。如果是正数, 则向右走。如果为负数, 则向左走。第二个数字是 Y 坐标。它告诉您如何使用 Y 轴。如果为正数, 则向上。如果为负数, 则向下走。

The vertex of a shape is the place where two sides of the shape come together. In general, when a shape is defined inside of a coordinate plane, it is defined by the vertices , and then the lines are drawn to connect them.
::形状的顶点是形状两面聚集的地方。一般来说, 当一个形状在坐标平面内被定义时, 它由顶点来定义, 然后绘制线条来连接它们。

A translation is when a figure or a point is slid on a coordinate grid from one place or another without changing its overall orientation.
::翻译是指数字或点从一个或另一个地方滑到坐标网格上时,不改变总方向。

In the figure above, the original point $\begin{aligned} A \end{aligned}$ is located at (-2, 3). Then it is translated to (4,1). $\begin{aligned} A^{'} \end{aligned}$ is the new point. What was the overall translation?
::在上图中,原点A位于(-2,3),然后被翻译为(4,1),A是新点。

First, figure out how many units $\begin{aligned} A \end{aligned}$ moved on the $\begin{aligned} x \end{aligned}$ axis
::首先,找出有多少单位 A 移动在 x 轴上

To find out, count the difference between the original point and the final point
::要找出答案, 计算原始点和最后点之间的差别

In this case, it is +6 units.
::在这种情况下,是+6单位。

Next, find how many units $\begin{aligned} A \end{aligned}$ moved on the $\begin{aligned} y \end{aligned}$ axis.
::下一步,找出在 y 轴上移动了多少个 A 单位。

If you count, you can see that it moved -2 units (remember that negative 'y' means down).
::如果计数,您可以看到它移动了 -2 个单位(记住负“y”是指向下移动)。

Then, put them together.
::然后把它们拼在一起。

The translation is (6, -2).
::翻译为6,2。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Reggie and his painted cat.
::早些时候,你得到一个问题关于雷吉和他画的猫。

First, he lightly sketches a coordinate grid over the picture.
::首先,他略微勾画了相片上的坐标网格。

Next, he determines that the cat basically fits in a rectangle and is made up of a circle and an oval. He lightly sketches a box around the original cat on the coordinate plane.
::接下来,他确定猫基本上处于矩形中,由圆形和奥瓦尔组成。他轻描淡写了一个盒子,围绕坐标平面上的原始猫。

Then, he finds the vertices of the original cat rectangle. They seem to be about (-11, -12), (-5, -12), (-11, -15), (-5, -15).
::然后,他发现了最初的猫形矩形的顶端。它们似乎在(11, -12),(5, -12),(11, -15),(5,15),(5,15)之间。

Then, he decides he wants the cat to go up 1 and over 9.
::然后,他决定,他想要猫上去1个和9个以上。

Then, he adds 9 to the x-coordinate of all of the vertices and adds 1 to the y-coordinates. This yields a new box with vertices (-2, -11), (4, -11), (-2, -14), (4, -14).
::然后,他把所有的脊椎的X座标加9个,在Y座标加1个。这产生一个带有脊椎的新盒子(2 - 11), (4, 11), (2 - 14), (4, 14)。

Finally, he draws this new box, and he sketches the cat shapes within it until it looks like a cat again. He erases the boxes, and his new cat is happy in its new place.
::最后,他画了这个新盒子, 他画了里面的猫形状, 直到它再次看起来像一只猫。他抹去盒子, 他的新猫在新的地方很开心。

Example 2
::例2

Calculate the following transformation numerically, and use a graph to check your answer.
::以数字方式计算随后的转换,并使用图表来检查您的回答。

A point is plotted at $\begin{aligned} (- 2, 1) \end{aligned}$ and then translated $\begin{aligned} (3, - 4) \end{aligned}$ , what are the coordinates of the translated point?
::一个点是用(-2,1)绘图的,然后翻译(3,-4),翻译点的坐标是多少?

First, add the x-coordinate of the original point to the x-coordinate of the transformation.
::首先,将原点的x坐标加到变换的x坐标上。

-2 + 3 = 1

Next, add the y-coordinate of the original point to the y-coordinate of the transformation.
::下一步,将原点的Y坐标加到转换的Y坐标上。

1 + (-4) = -3.

Then, write the resultant ordered pair.
::然后,写下随之而来订购的一对。

The answer is (1,-3).
::答案是(1,3)。

Finally, check your answer by graphing the original point and physically carrying out the transformation.
::最后,通过绘制原始点的图表和进行物理转换来检查你的答复。

Example 3
::例3

If the original point is located at (3,5) and is moved three units across and four units up, what are the coordinates of the final point?
::如果原点位于(3,5),并被移动到三个单位之间和四个单位上方,最后点的坐标是多少?

First, figure out the x translation.
::首先,找出 x 翻译。

"Across" is in the x-direction. Because it isn't otherwise stated, you can assume it is to the right, which is positive.
::“ 交叉” 在 X 方向中。因为没有另外说明, 您可以假设它是右边的, 这是积极的。

Next, add the x-translation to the initial x-coordinate to find the new x-coordinate.
::下一步,在初始 x 坐标上添加 x 译文,以查找新的 x 坐标。

3 + 3 = 6

Then, figure out the y translation.
::然后,找出y翻译。

It is four units up.
::四个单位向上。

Then, add that to the initial y-coordinate.
::然后,在最初的Y座标上加上这个。

4 + 5 = 9

Finally, write the resultant coordinate.
::最后,请写下相应的坐标。

The answer is $\begin{aligned} (6, 9) \end{aligned}$ .
::答案是(6,9).

Example 4
::例4

If the initial point is (-5,4) and the final point is (2,7) write the translation.
::如果起始点是(5,4),最后点是(2,7),则写译文。

First, find the x-translation.
::首先,找到X译文

-5 + ___ = 2 . In order to get from -5 to 2, the point must move 7 units to the right.
::- 5 + + = 2。为了从 - 5 到 2, 点必须向右移动 7 个单位。

Next, find the y-translation.
::下一个,找到Y翻译。

4 + ___ = 7 . In order to get from 4 to 7, the point must move up 3 units.
::4 + = 7 。为了从 4 到 7, 点必须往上移动 3 个单元。

Then, write the translation in words.
::那就把译文写成文字吧

The answer is 7 units to the right and 3 units up.
::答案是右边7个单元上面3个单元

Example 5
::例5

If a certain point is translated 2 units to the left and 4 units down, it is at the final point (-2, 6). What was the location of the original point?
::如果某一点向左翻译了2个单位,向下翻译了4个单位,则处于最后点(2个)。 6 原点的位置在哪里?

First, find the original x-coordinate by working backwards.
::首先,通过反向工作找到原始的x坐标。

2 units to the left means it is translated -2 on the x-axis. ___ + -2 = -2 The only coordinate that makes this work is 0.
::左侧 2 个单位表示它在 x 轴上翻译 - 2 。 _ + - 2 = - 2 表示此工作的唯一坐标为 0 。

Next, find the original y-coordinate the same way.
::接下来,找到原始的Y坐标以同样的方式。

4 units down means it is translated -4 on the y-axis. ___ + (-4) = 6 The original y-coordinate must be 10 to make this work.
::向下 4 个单位是指 Y 轴上的翻译 - 4 。 + + ( 4) = 6 。使这项工作得以进行, 原始的 Y 坐标必须是 10 个。

Then, write the original coordinate as an ordered pair.
::然后把原坐标写成一对订货

The answer is (0,10)
::答案是( 0, 10)

Finally, draw a graph with both the beginning and final point to check your work.

::最后,用开始点和最后点绘制一个图表来检查您的工作。

Review
::回顾

Write each translation in coordinate notation.
::将每一译文都写在协调符号中。

$\begin{aligned} A \end{aligned}$ to $\begin{aligned} A^{'} \end{aligned}$
::A至A ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

$\begin{aligned} B \end{aligned}$ to $\begin{aligned} B^{'} \end{aligned}$
::B至B ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

$\begin{aligned} C \end{aligned}$ to $\begin{aligned} C^{'} \end{aligned}$
::C至C = = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C = C

$\begin{aligned} D \end{aligned}$ to $\begin{aligned} D^{'} \end{aligned}$
::D至D _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

$\begin{aligned} E \end{aligned}$ to $\begin{aligned} E^{'} \end{aligned}$
::E至E _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

$\begin{aligned} F \end{aligned}$ to $\begin{aligned} F^{'} \end{aligned}$
::F至F __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

$\begin{aligned} G \end{aligned}$ to $\begin{aligned} G^{'} \end{aligned}$
::G至G+_____________________________________________

$\begin{aligned} H \end{aligned}$ to $\begin{aligned} H^{'} \end{aligned}$
::H至H __________________________________________________

$\begin{aligned} H \end{aligned}$ to $\begin{aligned} E \end{aligned}$
::H至E

$\begin{aligned} E \end{aligned}$ to $\begin{aligned} D \end{aligned}$
::E至D

$\begin{aligned} E^{'} \end{aligned}$ to $\begin{aligned} G \end{aligned}$
::英至G

$\begin{aligned} E^{'} \end{aligned}$ to $\begin{aligned} C \end{aligned}$
::E 至C

$\begin{aligned} B \end{aligned}$ to $\begin{aligned} A^{'} \end{aligned}$
::B至A ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

$\begin{aligned} B \end{aligned}$ to $\begin{aligned} G^{'} \end{aligned}$
::B至G _________________________________________________________________

$\begin{aligned} C^{'} \end{aligned}$ to $\begin{aligned} D^{'} \end{aligned}$
::C = 至 D _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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

章节大纲

常规

整数转换，点之间的路径

[Figure 1] ::[图1]

Translating Points on a Coordinate Plane ::坐标平面上的翻译点

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

::[图1]

Translating Points on a Coordinate Plane
::坐标平面上的翻译点

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