Course: 2.14坐标平面上的点

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坐标平面上的点
A map of a neighborhood block shows the corner of Brown Street and Smith Street. There is a house on the map marked with a black dot. The coordinates of this house need to be plotted correctly for the City Planner.
::附近街区的地图显示布朗街和史密斯街的拐角。地图上有一栋房屋有黑点标记。这栋房屋的坐标需要为市政规划员正确绘制。

In this concept, you will learn how to determine the coordinates of a point on a coordinate grid .
::在此概念中,您将学会如何确定坐标网格坐标点的坐标。

Coordinate Grid
::坐标网格

A coordinate grid is a graph used to locate points in space. A pair of numbers, called coordinates , tells where the point is in two-dimensional space.
::坐标网格是用于定位空间点的图表。一对数字,称为坐标,表示点在二维空间的位置。

Here is an example of a coordinate grid.
::以下是坐标网格的例子。

The horizontal axis , or the line that goes across side to side, is called the $\begin{aligned} x \end{aligned}$ axis . The vertical axis , or the line that goes up and down, is called the $\begin{aligned} y \end{aligned}$ axis . The point where the two axes meet is called the origin . The origin has the value of (0,0).
::水平轴,或横向对面的线,称为 x 轴。垂直轴,或向上和向下线,称为 y 轴。两个轴相交的点称为源。起源值为 0,0。

Every line on the $\begin{aligned} x \end{aligned}$ axis has a different value. The values start at 0 at the origin and continue on the horizontal axis. Each line has a value of 1. Every line on the $\begin{aligned} y \end{aligned}$ axis has a different value. The values start at 0 with the origin and continue on the vertical axis. Each line has a value of 1.
::x 轴上的每条线都有不同的值。值从 0 开始,然后在水平轴上继续。每条线的值为 1 。Y 轴上的每条线都有不同的值。值从 0 开始,然后在垂直轴上继续。每条线的值为 1 。

When a point has already been plotted on a coordinate grid, an ordered pair identifies its location. A coordinate is written in the form of an ordered pair. In an ordered pair, there are two numbers put inside a set of " data-term="Parentheses" role="term" tabindex="0"> parentheses . The first number is an $\begin{aligned} x \end{aligned}$ value and the second number is a $\begin{aligned} y \end{aligned}$ value $\begin{aligned} (x, y) \end{aligned}$ .
::当一个点已经绘制在坐标网格上时, 定购一对确定位置。坐标以定购一对的形式写成。在定购一对中, 将两个数字放在一组括号内。第一个数字是 x 值, 第二个数字是 y 值( x, y ) 。

Here is an example of an ordered pair:
::以下是一对定购夫妇的例子:

(3, 4)

This ordered pair has two values. It has an $\begin{aligned} x \end{aligned}$ value of 3 because the $\begin{aligned} x \end{aligned}$ value comes first. It has a $\begin{aligned} y \end{aligned}$ value of 4. Each ordered pair represents one point on a coordinate grid.
::这对定购夫妇有两个值。它的 x 值为 3 , 因为 x 值先到。它的 Y 值为 4 。每个定购夫妇代表坐标网格上的一个点。

This ordered pair can be plotted on the coordinate grid.
::这对定单夫妇可以在坐标网格上绘制。

To graph (3,4) on the grid, start at the origin and count three units on the $\begin{aligned} x \end{aligned}$ axis first. Then working from the 3, count up four since the $\begin{aligned} y \end{aligned}$ coordinate is four. That is where the point is plotted.
::在网格上的图( 3, 4) 中, 首先从原点开始, 然后在 x 轴上数三个单位。然后从 3 开始工作, 数四个, 因为 y 坐标是 4 。这是绘制点的位置。

Sometimes, the ordered pair contains a zero, for example:
::有时,定购的一对含有零,例如:

(0, 4)

This means that the $\begin{aligned} x \end{aligned}$ value is zero, so you don’t move along the $\begin{aligned} x \end{aligned}$ axis for your first point, instead you start counting up at zero. The $\begin{aligned} y \end{aligned}$ value is four, so you count up four units from zero.
::这意味着 x 值为 0, 这样您就不会在第一个点的 x 轴上移动, 而是开始以零计数。 y 值为 4, 所以从零数为四个单位。

The point actually falls directly on the $\begin{aligned} y \end{aligned}$ axis.
::点实际上直接落在 y 轴上。

Examples
::实例

Example 1
::例1

Earlier, you learned about a neighborhood map that shows a point of a house on the block.
::早些时候,你了解到一个街区地图显示一栋房子在街区的一角。

The city planner needs the coordinates of that house.
::城市规划员需要那栋房子的坐标

First, locate the point on the coordinate grid. There is only one point on this grid, so it is easy to identify.
::首先, 定位坐标网格上的点。这个网格上只有一个点, 所以很容易识别。

Next, look at where that point is located on the $\begin{aligned} x \end{aligned}$ axis. This map does not label values on each axis, so you will have to count out from the origin to determine the value. The $\begin{aligned} x \end{aligned}$ value is 2.
::下一步,请看该点位于 x 轴上的位置。本地图不为每个轴上标注值,因此您必须从源数中点出以决定值。 x 值为 2。

Then, look at where the point is located on the $\begin{aligned} y \end{aligned}$ axis. Again, there is no label for values on the map, so count up from the origin. The $\begin{aligned} y \end{aligned}$ value is 3.
::然后, 看看点位于 y 轴上的位置。同样, 地图上也没有值标签, 所以从源数上点数。 y 值为 3 。

The answer is (2,3). This is the coordinate pair for the house on the map.
::答案是(2,3) 这是地图上房子的坐标对

Example 2
::例2

Graph (9,3) on the coordinate grid.
::坐标网格上的图(9,3)

First, look at the $\begin{aligned} x \end{aligned}$ value in the ordered pair. The value is 9. This is the value on the horizontal axis. Starting at the origin, count across the horizontal axis to 9.
::首先,看看订购对的 x 值。值为 9 。这是水平轴上的值。从起始点开始, 横跨水平轴数到 9 。

Next, look at the $\begin{aligned} y \end{aligned}$ value. The value is 3. Starting at the 9 on the $\begin{aligned} x \end{aligned}$ axis, count up 3 units.
::下一步,看看 y 值。值是 3 。从 x 轴上的 9 开始, 计数为 3 个单位。

Then, mark the coordinate pair on the grid with a dot.
::然后在网格上用点标上坐标对

The answer goes on (9, 3) where the dot is.
::答案继续(9,3),点的位置。

Use the coordinate grid to answer the following questions.
::使用坐标网格回答下列问题。

Example 3
::例3

What is the ordered pair for point A?
::A点的订货配对是什么?

First, locate the point on the coordinate grid.
::首先,定位坐标网格上的点

Next, follow down to the $\begin{aligned} x \end{aligned}$ axis and write down the $\begin{aligned} x \end{aligned}$ value in the ordered pair.
::下一步, 跟随到 x 轴, 并写下定购一对中的 x 值。

Then, follow from the point over to the $\begin{aligned} y \end{aligned}$ axis and write down the $\begin{aligned} y \end{aligned}$ value in the ordered pair.
::然后,从点到 y 轴,写下 y 值。

The answer is (3,2)
::答案是(3,2)

Example 4
::例4

What is the ordered pair for point B?
::B点的订货配对是什么?

First, locate the point on the coordinate grid.
::首先,定位坐标网格上的点

Next, follow down to the $\begin{aligned} x \end{aligned}$ axis and write down the $\begin{aligned} x \end{aligned}$ value in the ordered pair.
::下一步, 跟随到 x 轴, 并写下定购一对中的 x 值。

Then, follow from the point over to the $\begin{aligned} y \end{aligned}$ axis and write down the $\begin{aligned} y \end{aligned}$ value in the ordered pair.
::然后,从点到 y 轴,写下 y 值。

The answer is (4,6)
::答案是(4,6)

Example 5
::例5

What is the ordered pair for point C?
::C点的订货配对是什么?

First, locate the point on the coordinate grid.
::首先,定位坐标网格上的点

Next, follow down to the $\begin{aligned} x \end{aligned}$ axis and write down the $\begin{aligned} x \end{aligned}$ value in the ordered pair.
::下一步, 跟随到 x 轴, 并写下定购一对中的 x 值。

Then, follow from the point over to the $\begin{aligned} y \end{aligned}$ axis and write down the $\begin{aligned} y \end{aligned}$ value in the ordered pair.
::然后,从点到 y 轴,写下 y 值。

The answer is (7,9)
::答案是(7,9)

Review
::回顾

Write the coordinates of each point.
::写下每个点的坐标。

A
::A A A

B
::BB ,B

C
::C 中 C

D
::D D

E
::英英英

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

I
::一一

J
::J J

K
::K K 级

L
::L L L

Graph and label each point on the coordinate grid.
::在坐标网格上标明每个点的图表和标签。

M(1, 3)
::M(1,3)

N(2, 4)
::N(2,4)

O(0, 6)
::O(0, 6)

P(8, 6)
::P(8)、P(8)、P(6)

Q(2, 2)
::问题(2,2,2)

R(4, 7)
:R4(4,7))

S(7, 7)
::S(7,7)

T(9, 0)
::T(9,0)

U(4, 6)
::U(4,6)

V(0, 5)
::VV(0, 5)

W(6, 8)
:W6,8)

Y(1, 7)
:1, Y1, 7)

Z(3, 4)
::Z(3,4) Z(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

General

坐标平面上的点

Coordinate Grid ::坐标网格

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

Coordinate Grid
::坐标网格

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