Section: 坐标平面中的点 | 4.17坐标平面中的点

Section outline

Megan is on vacation in Rome and is trying to find the restaurant where she will meet her friends for lunch. She got a map from her hotel that is formatted like a coordinate grid . The hotel is at the origin of the map and she was told that the restaurant is at the point $\begin{aligned} (4, 5) \end{aligned}$ on the map. How can Megan find this location on the map so she can make it to the restaurant?
::梅根正在罗马度假,正在寻找餐厅,在那里她会与朋友见面吃午饭。她从旅馆拿到一张地图,地图格式像坐标网一样。旅馆位于地图的源头,她被告知餐厅在地图上的点(4,5 ) 。梅根如何在地图上找到这个位置,以便她能到餐厅?

In this concept, you will learn how to name and graph ordered pairs of integer coordinates in a coordinate plane .
::在此概念中,您将学会如何在坐标平面上命名和图形显示订购的整数坐标对。

Naming and Graphing Points in the Coordinate Plane
::坐标平面中的命名和绘图点

The coordinate plane is a grid created by a horizontal number line, the $\begin{aligned} x \end{aligned}$ -axis , intersecting a vertical number line, the $\begin{aligned} y \end{aligned}$ -axis . The point of intersection is called the origin .
::坐标平面是一个由水平数字线、 x - 轴、垂直数字线、 y - 轴交叉组成的网格。交叉点称为源。

The coordinate plane allows you to describe locations in two-dimensional space.
::坐标平面允许您描述二维空间的位置。

Each point on the coordinate plane can be named by a pair of numbers called an ordered pair in the form $\begin{aligned} (x, y) \end{aligned}$ .
::坐标平面上的每个点可以用表格( x, y )中称为定购对的一对数字来命名。

The first number in an ordered pair identifies the $\begin{aligned} x \end{aligned}$ -coordinate of the point. This coordinate describes how far to the right or left of the $\begin{aligned} y \end{aligned}$ -axis a point is.
::定购一对中的第一个数字表示点的 x - 坐标。此坐标表示点在 y - 轴的右侧或左侧的距离。

The second number in an ordered pair identifies the $\begin{aligned} y \end{aligned}$ -coordinate of the point. This coordinate describes how far above or below the $\begin{aligned} x \end{aligned}$ -axis a point is.
::定购一对中的第二个数字表示点的 Y - 坐标。此坐标表示点在 x - 轴值上下有多远。

Here is an example.
::举一个例子。

Plot the point $\begin{aligned} (3, - 4) \end{aligned}$ on the coordinate plane.
::在坐标平面上标出点( 3, 4) 。

This point has an $\begin{aligned} x \end{aligned}$ -coordinate of 3 and a $\begin{aligned} y \end{aligned}$ -coordinate of -4.
::此点的 X - 坐标为 3 , y - 坐标为 - 4 。

To plot this point, first start at the origin.
::要绘制此点, 请先从源头开始。

Then, find the location of the $\begin{aligned} x \end{aligned}$ -coordinate. Because the $\begin{aligned} x \end{aligned}$ -coordinate is positive, you will be moving to the right. Move to the right along the $\begin{aligned} x \end{aligned}$ -axis 3 units until you find 3.
::然后找到 x - 坐标点的位置。因为 x - 坐标点是正的, 您将会向右移动。沿着 x - 轴 3 单位向右移动, 直到您找到 3 个单位。

Next, look at your $\begin{aligned} y \end{aligned}$ -coordinate. Because the $\begin{aligned} y \end{aligned}$ -coordinate is negative, you will be moving down. Move down from the 3 on the $\begin{aligned} x \end{aligned}$ -axis 4 units until you are lined up with the -4 on the $\begin{aligned} y \end{aligned}$ -axis.
::下一位请看您的 y - 坐标。因为 y - 坐标是负的, 您将会向下移动。从 x - 轴 4 的 3 向下移动, 直到您与 y - 轴的 - 4 排在一起。

The answer is shown plotted on the coordinate plane below.
::答案显示在下面的坐标平面上。

Here is another example.
::下面是另一个例子。

Give the ordered pair for the point plotted below.
::给下方绘图点的一对定购的配对。

To write the ordered pair you need both the $\begin{aligned} x \end{aligned}$ -coordinate and the $\begin{aligned} y \end{aligned}$ -coordinate.
::要写定购的一对, 您既需要 x - 坐标, 也需要 y - 坐标。

Start at the origin. You need to figure out how far to the right/left you need to move and then how far up/down you need to move to reach your point.
::开始于源头。您需要弄清楚您需要移动到右/ 左的距离, 以及您需要移动到上/ 下到哪里才能到达您的点。

First notice that you need to move 5 units to the right from the origin to reach the point. This means the $\begin{aligned} x \end{aligned}$ -coordinate is 5.
::第一个通知是,您需要将5个单位从源头移到右边才能到达点。这意味着 x - 坐标为 5 。

Next notice that you do not need to move up or down from the $\begin{aligned} x \end{aligned}$ -axis at all to reach the point. This means the $\begin{aligned} y \end{aligned}$ -coordinate is 0.
::下一个通知是,您不需要从 x - 轴向上或向下移动才能到达点。这意味着 y - 坐标为 0 。

The answer is that the ordered pair is $\begin{aligned} (5, 0) \end{aligned}$ .
::答案是,订购的一对是(5,0).

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Megan, who is on vacation in Rome.
::早些时候,你得到一个问题关于梅根, 谁在罗马度假。

She's at her hotel and trying to use a map to find the location of the restaurant where she will be meeting her friends for lunch. The restaurant is at the point $\begin{aligned} (4, 5) \end{aligned}$ on the map.
::她正在她的旅馆里,试图用一张地图找到餐厅的地址,在那里她将与朋友见面吃午饭。在地图上,餐厅位于点(4、5)。

This point has an $\begin{aligned} x \end{aligned}$ -coordinate of 4 and a $\begin{aligned} y \end{aligned}$ -coordinate of 5.
::此点有 x - 坐标 4 和 y - 坐标 5 。

To find this point, Megan should start at the origin on the map (her hotel).
::为了找到这一点,Megan应从地图(她的旅馆)的原产地开始。

Then, she should find the location of the $\begin{aligned} x \end{aligned}$ -coordinate. Because the $\begin{aligned} x \end{aligned}$ -coordinate is positive, she will be moving to the right. She needs to move to the right 4 units until she reaches the 4 on the $\begin{aligned} x \end{aligned}$ -axis.
::然后,她应该找到x - 坐标的位置。因为x - 坐标是正的, 她会向右移动。她需要移动到正确的 4 个单位, 直到她到达 X - 轴上的 4 个单位。

Next, Megan should look at her $\begin{aligned} y \end{aligned}$ -coordinate. Because the $\begin{aligned} y \end{aligned}$ -coordinate is positive, she will be moving up. She should move up 5 units from the 4 on the $\begin{aligned} x \end{aligned}$ -axis.
::梅根应该看看她的Y座标,因为Y座标是正的, 她会向上移动。她应该从x轴的4号上移5个单元。

The answer is shown plotted on the coordinate plane below.
::答案显示在下面的坐标平面上。

Example 2
::例2

This coordinate grid shows locations in Jimmy’s city. Name the ordered pair that represents the location of the city park.
::这个坐标网格显示Jimmy所在城市的位置。命名代表城市公园位置的一对定购夫妇。

To write the ordered pair you need both the $\begin{aligned} x \end{aligned}$ -coordinate and the $\begin{aligned} y \end{aligned}$ -coordinate.
::要写定购的一对, 您既需要 x - 坐标, 也需要 y - 坐标。

Start at the origin. You need to figure out how far to the right/left you need to move and then how far up/down you need to move to reach your point.
::开始于源头。您需要弄清楚您需要移动到右/ 左的距离, 以及您需要移动到上/ 下到哪里才能到达您的点。

First notice that you need to move 2 units to the left from the origin in order to be exactly above the point for the city park. This means the $\begin{aligned} x \end{aligned}$ -coordinate is -2.
::首先通知您需要将2个单位从原点移到左边,才能完全超过城市公园的点。这意味着 x - 坐标是 - 2 。

Next notice that you need to move down 6 units from the -2 on the $\begin{aligned} x \end{aligned}$ -axis to reach the point. This means that the $\begin{aligned} y \end{aligned}$ -coordinate is -6.
::下一个通知, 您需要从 X - 轴上的 - 2 向下移动 6 个单位才能到达点。这意味着 y - 坐标是 - 6 。

The arrows below show how you should have moved your finger to find the coordinates.
::下面的箭头显示您应该如何移动手指来找到坐标。

The answer is that the ordered pair for the city park is $\begin{aligned} (- 2, 6) \end{aligned}$ .

Example 3
::例3

Plot the point $\begin{aligned} (0, 3) \end{aligned}$ on the coordinate plane.
::在坐标飞机上标出点( 0, 3) 。

This point has an $\begin{aligned} x \end{aligned}$ -coordinate of 0 and a $\begin{aligned} y \end{aligned}$ -coordinate of 3.
::此点的 X - 坐标为 0 , y - 坐标为 3 。

To plot this point, first start at the origin.
::要绘制此点, 请先从源头开始。

Then, find the location of the $\begin{aligned} x \end{aligned}$ -coordinate. Because the $\begin{aligned} x \end{aligned}$ -coordinate is 0, you do not need to move to the right or to the left from the origin. Stay at the origin.
::然后找到 x - 坐标的位置。因为 x - 坐标是 0, 您不需要移动到源头的右侧或左侧。请留在源头。

Next, look at your $\begin{aligned} y \end{aligned}$ -coordinate. Because the $\begin{aligned} y \end{aligned}$ -coordinate is positive you will be moving up. Move up from the origin 3 units until you are lined up with the 3 on the $\begin{aligned} y \end{aligned}$ -axis.
::下一位请看您的 y - 坐标。因为 y - 坐标是肯定的, 您将会向上移动。从源 3 单位上移, 直到您与 y - 轴上的 3 组排在一起。

The answer is shown plotted on the coordinate plane below.
::答案显示在下面的坐标平面上。

Example 4
::例4

Give the ordered pair for the point plotted below.
::给下方绘图点的一对定购的配对。

To write the ordered pair you need both the $\begin{aligned} x \end{aligned}$ -coordinate and the $\begin{aligned} y \end{aligned}$ -coordinate.
::要写定购的一对, 您既需要 x - 坐标, 也需要 y - 坐标。

Start at the origin. You need to figure out how far to the right/left you need to move and then how far up/down you need to move to reach your point.
::开始于源头。您需要弄清楚您需要移动到右/ 左的距离, 以及您需要移动到上/ 下到哪里才能到达您的点。

First notice that you need to move 6 units to the right from the origin to be exactly above the point. This means the $\begin{aligned} x \end{aligned}$ -coordinate is 6.
::第一个通知是,您需要将 6 个单位从源头移到右侧, 才能完全超过点。这意味着 x - 坐标是 6 。

Next notice that you need to move down 3 units from the 6 on the $\begin{aligned} x \end{aligned}$ -axis to reach your point. This means your $\begin{aligned} y \end{aligned}$ -coordinate is -3.
::下一个通知, 您需要从 X - 轴的 6 上向下移动 3 个单位, 才能到达您的点。这意味着您的 y - 坐标是 - 3 。

The answer is that the ordered pair is $\begin{aligned} (6, - 3) \end{aligned}$ .
::答案是,订购的一对是(6, - 3) 。

Example 5
::例5

Plot the point $\begin{aligned} (- 2, - 5) \end{aligned}$ on the coordinate plane.
::在坐标平面上标出点数(-2,-5)。

This point has an $\begin{aligned} x \end{aligned}$ -coordinate of -2 and a $\begin{aligned} y \end{aligned}$ -coordinate of -5.
::此点的 X - 坐标为 - 2, y - 坐标为 - 5。

To plot this point, first start at the origin.
::要绘制此点, 请先从源头开始。

Then, find the location of the $\begin{aligned} x \end{aligned}$ -coordinate. Because the $\begin{aligned} x \end{aligned}$ -coordinate is negative, you will be moving to the left. Move to the left 2 units until you reach the -2 on the $\begin{aligned} x \end{aligned}$ -axis.
::然后找到 x - 坐标的位置。因为 x - 坐标为负, 您将会向左移动。移动到左边 2 个单位, 直到您在 x - 轴上到达 - 2 。

Next, look at your $\begin{aligned} y \end{aligned}$ -coordinate. Because the $\begin{aligned} y \end{aligned}$ -coordinate is negative, you will be moving down. Move down 5 units from the -2 on the $\begin{aligned} x \end{aligned}$ -axis.
::下一位请看您的 y - 坐标。因为 y - 坐标为负, 您将会向下移动。从 x - 轴的 - 2 向下移动 5 个单位。

The answer is shown plotted on the coordinate plane below.
::答案显示在下面的坐标平面上。

Review
::回顾

Name the ordered pair that represents each of these points on the coordinate plane.
::列出代表坐标平面上每个点的一对定购的对。

Below is a map of an amusement park. Name the ordered pair that represents the location of each of these rides.

roller coaster
::过山车

Ferris wheel
::摩轮轮轮

carousel
::旋转木体

log flume
::圆木烟云

Name the ordered pairs that represent the vertices of triangle FGH.
::列出代表三角形FGH的顶点的订购对。

F
::F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F

G
::G 级

H
::赫时

Name the ordered pairs that represent the vertices of pentagon ABCDE.
::列出代表五角形ABCDE顶点的订购对。

A
::A A A

B
::BB ,B

C
::C 中 C

D
::D D

E
::英英英

On the grid below, plot point $\begin{aligned} V \end{aligned}$ at $\begin{aligned} (- 6, 4) \end{aligned}$ .
::在下面的网格上,第5点(-6,4)处。

On the grid below, plot point a triangle with vertices $\begin{aligned} R (4, - 1), S (4, - 4) \end{aligned}$ and $\begin{aligned} T (- 3, - 4) \end{aligned}$ .
::在下面的网格上,地块指向一个三角形,有脊椎R(4, - 1),S(4, - 4)和T(3, - 4)。

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

Naming and Graphing Points in the Coordinate Plane ::坐标平面中的命名和绘图点

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

Naming and Graphing Points in the Coordinate Plane
::坐标平面中的命名和绘图点

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