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  • 对坐标平面的对称

    Symmetry in Art
    ::艺术的对称性

    lesson content
    Symmetry Art

    has been at the heart of artistic works for as long as humans have made art. In the interactive below, you will draw designs on the screen and reflect it across different parts of the coordinate system to observe its symmetry.
    ::艺术作品一直是艺术作品的核心。 在下文的互动中,你将在屏幕上绘制设计图,并在协调系统的不同部分反映出来,以观察对称性。

     

     

    Discussion Questions:
    ::讨论问题:

    1. Make a point at (3,4) and reflect it over the x−axis. What are the coordinates of the new point? What do the points have in common, what is different?
      ::点数( 3, 4) , 然后在 x - 轴上反射 。 新点的坐标是什么 ? 这些点有什么共同点, 有什么不同 ?
    2. Make a point at (2,5) and reflect it over the y−axis. What are the coordinates of the new point? What do the points have in common, what is different?
      ::在 y- 轴 上画一个点 ( 2, 5) , 并将其反射到 y- 轴 上。 新点的坐标是什么 ? 这些点有什么共同点, 有什么不同 ?
    3. Make a point at (1,3) and reflect it into all four quadrants . What are the coordinates of the new points? What do the points have in common, what is different?
      ::点数( 1, 3) , 并将其反射到所有四个四方位。 新点的坐标是多少? 这些点有什么共同点, 有什么不同?

     

    Facial Recognition Software
    ::辅助识别软件

    lesson content
    Using Dots to Map Faces

    Facial recognition software uses properties of facial symmetry to identify people. The 3-dimensional relationships between distinct points on our face act as a sort of unique “fingerprint” that can be used to identify us.
    ::面部识别软件使用面部对称特性来识别人。 我们面部不同点之间的三维关系是一种独特的“指印 ” , 可以用来识别我们的身份。

    For this interactive, you will identify how coordinates reflect across the y-axis .
    ::对于此互动, 您将确定坐标如何在 Y 轴上反射 。

     

     

     

     

     

    Make a Rectangle
    ::矩形

    Steven is trying to form a rectangle on the coordinate plane below, but only has one of the vertices . Help him find the remaining points. Using this interactive, you will practice finding the coordinates of the rectangle’s vertices by reflecting the coordinate of the point you know across the x- and y-axis.
    ::Steven正试图在下面的坐标平面上形成矩形, 但只有一个顶点 。 帮助他找到剩余点 。 使用此互动方式, 您将练习通过反映您所知道的横跨 X 和 Y 轴点的坐标来找到矩形顶点的坐标 。

     

     

    Discussion Questions:
    ::讨论问题:

    1. What do you notice about all the vertices?
      ::你注意到所有脊椎是什么?
    2. Could you have predicted where the remaining points would be without using the graph?
      ::如果不用图表,你能预测剩下的点会在哪里吗?
    3. If one point is (1, 3) how would you form a rectangle on the plane without plotting on a coordinate plane?
      ::如果一个点是(1, 3), 你如何在飞机上形成矩形而不在坐标飞机上图谋?
    4. How are reflections in the coordinate plane similar to or different from opposite numbers on the number line?
      ::坐标平面上的反射如何与数字线上的反射数字相似或不同?

     

    Making a Robot Part 7
    ::使机器人第7部分成为第7部分

    The functions of a robot have been improved across activities in a number of lessons, starting with , The next improvement is to modify the reset() command to function in two dimensions .  At this point, the robot accepts the following commands:
    ::机器人的功能在许多课程中得到了改进, 从 开始, 下一个改进是修改重置() 命令, 使其在两个维度中发挥作用。 此时此点, 机器人接受以下命令 :

    • stepsYNo - This command will move the robot n steps forward, or n steps backward. The command stepsY(4) will move the robot 4 steps forward, and the command stepsY(-2) will move the robot 2 steps backward.
      ::stepsYNo - 此命令将移动机器人 n 步向前, 或 n 步向后。 命令步骤Y(4) 将移动机器人 4 步向前, 命令步骤Y( 2) 将移动机器人 2 步向后。
    • stepsXNo - This command will move the robot n steps right, or n steps left. The command stepsX(4) will move the robot 4 steps right, and the command stepsX(-2) will move the robot 2 steps left.
      ::stecXNo - 此命令将移动机器人 n 步向右, 或 n 步向左。 命令 stepsX(4) 将移动机器人 4 步向右, 命令 stepsX( 2) 将移动机器人 2 步向左 。
    • location() - This command returns two values, telling you the current x-location and y-location of the robot.
      :sad) 位置 - 此命令返回两个值, 告诉您机器人的 x 位置和 Y 位置 。

    How can you apply knowledge of opposites and coordinate planes to reset the robot in two dimensions?
    ::您如何应用对反面知识, 并协调平面将机器人重置为两个维 ?

    In the following interactive, you will move a robot vertically and horizontally around a coordinate plane and then use coordinates to describe its location on the grid.
    ::在接下来的互动中,您将垂直和水平地移动机器人到坐标平面上,然后使用坐标来描述机器人在网格上的位置。

     

     

     

     

    Discussion Questions
    ::讨论问题 讨论问题

    1. The next step is to build a reset function that will return the robot from any location to its starting position of 0. What would this function look like in two dimensions? How would the function return the robot from any location to its starting position?
      ::下一步是建立一个重置函数, 将机器人从任何位置返回到零的起始位置。 这个函数在两个维度中会是什么样子 ? 该函数如何将机器人从任何位置返回到起始位置 ?
    2. What would the original one-dimensional reset() command do in two dimensions?
      ::最初的一维重置命令在两个维度中能做什么?
      Summary
    • When a point is reflected over the x-axis, find the opposite of the y-coordinate, ( x , y ) → ( x , − y ) . For example:  ( 1 , − 2 ) → ( 1 , 2 )  
      ::当 X 轴反射一个点时, 找到 Y 坐标的对面, (x, y) (x, y) (x, y) 。 例如 : (1, − 2) (1, 2) (1, 2) 等
    • When a point is reflected over the y-axis, find the opposite of the x-coordinate,  ( x , y ) → ( − x , y ) . For example:  ( 1 , − 2 ) → ( − 1 , 2 )  
      ::当 Y 轴反射一个点时, 找到与 x 坐标相反的点, (x,y) (- x,y) (- x,y) 。 例如 : (1, − 2) (-1, 2) 等