几何相称性:缩放绘图

Scale Drawings
::缩放绘图

In this lesson, you will be applying ratios and proportional relationships to geometry. A scale drawing is a drawing that is to scale of an original image .
::在此教训中, 您将会对几何应用比例和比例关系 。 比例图的绘制就是对原始图像的缩放 。

When an object is "to scale," that means it is the same shape, but not the same size. If an actual bee is 0.5 inches in length, and the drawing is 2 inches, then the scale factor would be 4 because 4 times 0.5 equals 2. The scale factor is the amount that an image is enlarged or shrunk. It is also called $\begin{array}{r}k\end{array}$  because $\begin{array}{r}k\end{array}$  represents the multiplier between two proportional ratios and scale drawings represent proportional relationships. This is an example of a scale drawing.  Notice all the lines, curves, and points preserve proportionality.
::当对象为“ 缩放 ” 时, 意指它的形状相同, 但大小不同。 如果实际蜜蜂的长度为0. 5 英寸, 绘图为 2 英寸, 那么比例系数为 4, 因为 4 乘以 0.5 等于 2. 比例系数是 图像放大或缩放的数值。 缩放系数也称为 k , 因为 k 代表两个比例比和比例图绘制之间的乘数代表比例关系。 这是一个比例图的示例。 注意所有线条、 曲线和点保持比例性 。

播放段落

This is an example when proportions are not preserved. The result is a skewed bee and not a scale drawing.
::这是比例没有被保持的例子。 结果是一只斜蜜蜂, 而不是一个比例图 。

  

Brainy's Curiosity
::春雨的好奇心

Brainy  is very curious. He wants to know what happens to his picture when it gets enlarged and shrunk on a photo printing website.  He starts playing around with the website and notices some correlations between the numbers and the sizes of his original photo and the duplicates.  
::布鲁德非常好奇。 他想知道照片扩大后照片会怎样,并缩小到照片印刷网站。 他开始与网站玩耍,注意到他原始照片和复制照片的数字和大小之间的一些关联。

播放段落
• Take Brainy's photo and enlarge it and shrink it. See what sort of conclusions you can make about scale drawings.
  ::拍摄布温的照片,放大并缩小它。看看您可以对比例图画做出什么样的结论。
播放段落
• Determine what the scale factor would be if he started with an 8" by 8" photo and made a duplicate of 6" by 6."
  ::确定比例系数是多少 如果他以8乘8开始 并复制6乘6"。"

As was shown in the interactive, the scale factor is found by putting the copy (or duplicate) into a ratio with the original image :   $\begin{array}{r}k=\frac{\text{copy}}{\text{original}}.\end{array}$  If you know the length of two corresponding sides, then you can determine the scale factor.
::如互动中所示,通过将复制件(或复制件)与原始图像( k=复制原版) 的比率相匹配,可以发现比例系数。如果知道对应两边的长度,那么可以确定比例系数。

Drawing Bedrooms
::绘图房

Tiana wants to rearrange the furniture in her bedroom. She knows that it is 12 feet by 10 feet, with a door and window on the opposite wall. In her bedroom, she needs her bed, a desk, bookshelf, dresser, and chair. She is drawing a scale mapping on graph paper and decides to make 1 foot = 2 squares (0.50 inch).  Use the interactive to rearrange her furniture. 
::蒂安娜想重新安排卧室的家具。 她知道卧室是12英尺乘10英尺,墙对面有扇门和窗户。 在卧室,她需要她的床、桌子、书架、梳妆台和椅子。 她正在图纸上绘制比例图,决定用1英尺=2平方(0.50英寸)。 使用互动来重新安排家具。

Discussion Question
::讨论问题

Visualize your own bedroom, and draw a scale drawing of i t . Discuss the process and challenges of designing a bedroom layout. for other examples of scale drawings!
::将自己的卧室视像化, 并绘制一个比例图 。 讨论设计卧室布局的过程和挑战 。 其他比例图的例子 !