章节大纲

  • Maps
    ::地图地图地图

    Distance on the coordinate plane is used in real-world situations involving cell phones, computers, GPS, and other technologies.
    ::在涉及手机、计算机、全球定位系统和其他技术的现实世界局势中,使用坐标平面上的距离。

    Use the simplified map of a real city below to  estimate the distance between two locations of your choosing. Each square on the map grid is about 250 feet across.
    ::使用下面一个城市的简化地图来估计您所选择的两个地点之间的距离。 地图网格上的每个方位大约宽250英尺。

    It is easier to estimate the distance between two places with either the same number ( y axis) coordinates , or the same letter ( x axis) coordinates. Why?
    ::比较容易估计数字相同(y-axis)座标或字母相同(x-axis)座标的两个位置之间的距离。 为什么?

    lesson content

    Discussion Questions:
    ::讨论问题:

    1. Cynthia and Jerome are going from the library (brown) to the post office (dark blue), shown in the map above. The GPS says the distance is 1.5 miles. Cynthia believes that the distance is based on the distance that you travel on the roads. Jerome thinks that the distance is based on the straight line distance between the two locations. Who do you think is correct? How could you answer this question using tools? What tools would be needed?
      ::Cynthia和Jerome正在从图书馆(褐色)到邮局(黑蓝色),上面的地图显示。GPS说距离是1.5英里。Cynthia认为距离是基于你在公路上的距离。 Jerome认为距离是基于两个地点之间的直线距离。你认为谁是正确的?你如何用工具回答这个问题?需要什么工具?
    2. Where does the GPS program get the numbers used to find the distance?
      ::GPS程序从哪弄来 用来找到距离的号码?
    3. Do you think the fact that the earth is spherical influences the way that the GPS program calculates distance?
      ::你认为地球是球体这一事实 会影响GPS程序计算距离的方式吗?

     


     Distance on the Coordinate Plane
    ::坐标平面上的距离

    lesson content
    Coordinate Plane

    Discussion Questions
    ::讨论问题 讨论问题

    1. What is the distance between the points in the image above?
      ::上面图像的点之间的距离是多少 ?
    2. What information is needed to find the distance between two points on a coordinate plane? 
      ::需要何种信息才能找到坐标飞机上两点之间的距离?

    When two points on a coordinate plane have the same x coordinate or y coordinate, we can find the distance by counting the units between points. We can use the numbers on the x axis and y axis to help determine the distance. Two points with the same x coordinate will run parallel to the y axis number line which we can use to help determine the distance. Two points with the same y-coordinate will run parallel to the x axis number line which we can use to help determine the distance.
    ::当坐标平面上的两点具有相同的 x - 坐标或 y - 坐标时, 我们可以通过点之间的单位数来找到距离。 我们可以使用 x - 轴和 y - 轴的数字来帮助确定距离。 同一 x - 坐标的两点将和用来帮助确定距离的 y - 轴号线平行。 同一 Y 坐标的两点将和用来帮助确定距离的 x - 轴号线平行。

    In this interactive, you will measure distance between houses by using points on a coordinate plane.
    ::在此互动中,您将使用坐标平面上的点数测量房屋之间的距离。

     

    INTERACTIVE
    Distance Between Two Points: Biking the Blocks
    minimize icon

    Dave bikes from his house, which is at (5, 6) on the map, to his friend's house at (5, 5).  From his friend's house, he bikes to school at (5, 2).
    ::从地图上(5,6)处他家的戴夫自行车,到他朋友家(5,5)处(5,5)处,从他朋友家骑自行车到5,2上学。

    • Move the red point to help you trace Dave's path. The red point shows Dave's position.
      ::红点显示戴夫的位置
    • Each other point indicates the location of a building.
      ::每一点标明建筑物的位置。
    Your device seems to be offline.
    Please check your internet connection and try again.

    +
    Do you want to reset the PLIX?
    Yes
    No

     

     

     

    Discussion Questions
    ::讨论问题 讨论问题

    1. Graph and find the distance of the points (5,1) and (5,5). Is it possible to find the distance between these points without graphing them on a coordinate plane?
      ::图表并找到点(5,1)和点(5,5)之间的距离(5,5),能否找到这些点之间的距离而不在坐标平面上绘制图表?
    2. Graph and find the distance of the points (-2,2) and (3,2). How would we find the distance when the points are in different quadrants ?
      ::并找到点( 2, 2) 和点( 3, 2) 的距离。 当点位于不同的四分位数时, 我们如何找到点的距离 ?

     


    Distance on the Coordinate Plane Part 2
    ::坐标平板距离第2部分

    When two points share an x coordinate or y coordinate,  you can find the distance by looking at the other coordinates which are not the same.
    ::当两个点共用 x - 坐标或 y - 坐标时,您可以通过查看其他不相同的坐标找到距离。

    Using this interactive, you will practice finding the distance between two points on the coordinate plane with the same x  or y  value.
    ::使用此互动方式, 您将练习找到坐标平面上两点之间的距离, 与 x 或 y 值相同 。

     

    INTERACTIVE
    Distance on the Coordinate Plane
    minimize icon
    • Enter the distance between the given points in the box.
      ::输入框中给定点之间的距离。
    • Click the buttons for a hint and to change the points.
      ::单击按钮以获取提示并更改点。
    Your device seems to be offline.
    Please check your internet connection and try again.

    +
    Do you want to reset the PLIX?
    Yes
    No

     

     

    oints-in-the-coordinate-plane" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f45a49cc880412d4da0712d&collectionHandle=algebra&collectionCreatorID=3&conceptCollectionHandle=algebra-:吐舌头oints-in-the-coordinate-plane&mode=lite" test-id="5f45a49cc880412d4da0712d">

     

     


    Interpreting Distance on a Coordinate Plane
    ::在坐标平面上解释距离

    There are many situations where the d istance between two points on a coordinate plane does not represent a physical distance.
    ::在许多情况下,坐标飞机上两点之间的距离并不代表实际距离。

    City
    ::城市城市

    Elevation (ft)
    ::电梯(ft)

    Avg Low Temperature in January (C)
    ::1月低温(C)

    Point on the Graph
    ::图表的点

    Harber, CA
    ::加利福尼亚州哈贝尔

    -16

    5

     (-16, 5)

    Holtville, CA
    ::加利福尼亚州霍尔特维尔

    -10

    4

    (-10, 4) 

    New Orleans, LA
    ::新奥尔良,洛杉矶

    -7

    8

    (-7, 8) 

    Albany, NY
    ::纽约奥尔巴尼

    2

    -10

    (2, -10) 

    Mobile, AL
    ::ALAL,流动

    10

    6

    (10, 6) 

    Miami, FL
    ::佛罗里达州迈阿密

    7

    15

    (7, 15)  

    For this interactive, you will be plotting points based on the x   and y coordinates in the table above.
    ::对于此互动, 您将根据上表中的 x 和 y 坐标绘制点 。

     

    INTERACTIVE
    Interpreting Distance on a Coordinate Plane
    minimize icon
    • Drag the points on the plane according to the data on average low temperatures in January from the table.
      ::拖曳平面上的点数,根据1月份从表格中得出的平均低温数据。
    Your device seems to be offline.
    Please check your internet connection and try again.

    +
    Do you want to reset the PLIX?
    Yes
    No

     

     

     

     


    Coordinate Plane Puzzle
    ::坐标平面谜

    In the interactive below, you will try to solve a puzzle by plotting coordinates that satisfy the given requirements.
    ::在下文互动中,您将尝试通过绘制符合特定要求的坐标来解决谜题。

     

    INTERACTIVE
    Coordinate Plane Puzzle
    minimize icon

    Drag the points according to the riddle below. Press the button that appears to check your work.
    ::根据下面的谜题拖曳点。 按下检查您工作的按钮 。

    • Point X  is located at  ( 2 , 5 ) .
      ::X点位于(-2、-5点)。
    • Point A  is 6 units away from  X .  
      ::A点离X有6个单位
    • Point B  is 5 units away from   A .  
      ::B点离A点5个单位
    • Point   B    has a  y  -value of 0
      ::B点的Y值为0。
    • Point C  is 9 units away from  B .  
      ::C点离B点有9个单位
    • Point C  has an  x value of 5 .
      ::C点的 x - 值为 - 5 。
    Your device seems to be offline.
    Please check your internet connection and try again.

    +
    Do you want to reset the PLIX?
    Yes
    No

     

     

    oints-in-the-coordinate-plane" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f45a4ac63b288dadee409a2&collectionHandle=algebra&collectionCreatorID=3&conceptCollectionHandle=algebra-:吐舌头oints-in-the-coordinate-plane&mode=lite" test-id="5f45a4ac63b288dadee409a2">
      Summary
    • When two points share an x-coordinate or y-coordinate, you can find the distance between the two numbers of other coordinate.
      ::当两个点共用 x 坐标或 Y 坐标时,您可以找到其他坐标的两个数字之间的距离。
    • For example, The distance between (1,2) and (1, -4) is 6 because the distance between 2 and -4 is 6.
      ::例如,(1,2)和(1,4)之间的距离是6,因为2和4之间的距离是6。