协调计划变序顺序

Get ready for the big time!
::准备好迎接大日子!

Before  you begin combining the rigid motions into sequences, quickly review the rules for each one.
::在你开始把僵硬的动作 合并为顺序之前, 快速审查每个规则。

Translations
::笔译翻译

To translate an object on a coordinate plane , identify how much the object is going to move up or down as well as left or right. To translate  $\begin{align*}a\end{align*}$  units right and  $\begin{align*}b\end{align*}$  units up, use the notation  $\begin{align*}A (x, y) → A' (x + a, ~y + b).\end{align*}$
::要在坐标平面上翻译对象, 请标明对象向上或向下移动的次数, 以及向左或向右移动的次数。 要向右和向上翻译一个单位和 b 单位, 请使用 A( x, y) 的符号 A*A( x+a, y+b) 。

Reflections
::反思

To reflect an object on a coordinate plane , first identify where the mirror line is. To reflect over the $\begin{align*}x\text{-}\end{align*}$ axis , j ust multiply the $\begin{align*}y\end{align*}$  coordinate of the point by -1. U se the notation  $\begin{align*}A (x, y) → A' (x, ~ \text{-}y).\end{align*}$   Similarly, t o reflect over the $\begin{align*}y\text{-}\end{align*}$ axis, multiply the $\begin{align*}x\end{align*}$  coordinate of the point by -1. Use the notation  $\begin{align*}A (x, y) → A' (\text{-}x, y). \end{align*}$
::要在坐标平面上反射对象, 请先确定镜像线的位置。 要在 X 轴上反射, 请将点的 Y 坐标乘以-1。 使用 符号 A( x,y) {A} {A} (x, -y) 。 类似地, 要在 y 轴上反射, 请将点的 x 坐标乘以 - 1 。 请使用 符号 A( x,y) {A} (x,y) {A} (x) 。

Rotations
::轮调

To rotate an object, identify where the center of rotation is and how many degrees to rotate the object.  You can rotate a point 90°, 180°, or 270° around the origin using the following rules:
::要旋转对象,请标明旋转中心的位置和旋转对象的度。您可以使用下列规则在原点周围旋转90°、180°或270°:

Identifying Sequences of  Rigid Motions
::确定僵硬动议的顺序

Here you  will explore sequences of  rigid motions on the coordinate plane. A sequence of rigid mo tions is two or more translations, reflections or rotations performed one after another.
::这里您将探索坐标平面上的僵硬动议顺序。 僵硬动议的顺序是两个或两个以上翻译、 反射或轮流执行。

Use the interactive below to see if you can map one shape onto another to figure out the sequence of rigid motions .
::使用下面的交互效果来查看您能否将一个形状映射到另一个形状, 以找出僵硬动作的顺序 。

Discussion Question
::讨论问题

Predicting Sequences of Rigid Mo tions
::僵硬动议的预测序列

To perform a sequence of rotations all  you have to do is perform each rigid motion one at a time, in order.  Use the interactive below to practice sequences involving all of the rigid motions we have learned thus far.
::要进行一系列的旋转, 您只需要按顺序一次执行每个僵硬的动作。 使用下面的交互动作来练习涉及我们到目前为止所学到的所有僵硬动作的顺序 。

Just as a reminder, here are the from above:
::以示教诲。这是从上面降示的:

Example
::示例示例示例示例

Given the point $\begin{align*}A,\end{align*}$  located at $\begin{align*}(4, 1)\end{align*}$ , reflect $\begin{align*}A\end{align*}$ over the $\begin{align*}x\text{-}\end{align*}$ axis and then translate the resulting point 3 units left. Write the coordinate of the new point, $\begin{align*}A’\end{align*}$ .
::考虑到位于(4,1)的A点,反映Aover x轴,然后翻译剩余的3点单位。写出新点的坐标,A_。

You  know that to reflect $\begin{align*}A\end{align*}$  over the $\begin{align*}x\text{-}\end{align*}$ axis,  you can just change the sign of the $\begin{align*}y\end{align*}$  coordinate: $\begin{align*}(4,1) → (4,-1)\end{align*}$ . To translate a shape 3 units to the left, subtract 3 from the $\begin{align*}x\end{align*}$  coordinate :   $\begin{align*}(4,-1) → (1, -1)\end{align*}$ .
::要在 x 轴上反射 A, 您可以更改 Y 坐标的符号 : (4, 1)\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ 将形状 3\\\\\\\\\\\\ x \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

Answer: $\begin{align*}A’\end{align*}$ will be located at  $\begin{align*}(1,-1)\end{align*}$  
::答复:A`将位于(1,-1)

Example
::示例示例示例示例

Given the triangle $\begin{align*}ABC,\end{align*}$  with points $\begin{align*}A (1, 3), B (-2, 2),\end{align*}$  and $\begin{align*} C (4, 0),\end{align*}$  rotate $\begin{align*}ABC\end{align*}$   180° c lockwise and translate the resulting triangle 5 units down.
::根据三角形ABC, 包括点A(1,3)、B(-2,2)和C(4,4,0), 旋转ABC 180°时钟, 并将由此产生的三角形 5 单位向下翻译 。

Write the coordinates of the new shape $\begin{align*}A’B’C’\end{align*}$ .
::写下新形状的坐标 A_B_C_

You  know that to rotate a point 180° clockwise, you  change the sign of both the $\begin{align*}x\end{align*}$  coordinate and the $\begin{align*}y\end{align*}$  coordinate:
::要旋转180°的时速,您必须改变 x 坐标和 y 坐标的标志:

• (1, 3) → (-1, -3)
• (-2, 2) → (2, -2)
• (4, 0) → (-4, 0)

To translate a shape 5 units down, subtract 5 from the $\begin{align*}y\end{align*}$  coordinate.
::要将形状 5 单位向下翻译, 请从 Y 坐标中减去 5 个 。

• (-1, -3) → (-1, -8)
• (2, -2) → (2, -7)
• (-4, 0) → (-4, -5)

Answer: Shape $\begin{align*}A’B’C’\end{align*}$  will be located at $\begin{align*}A’ (-1, -8), B’ (2, -7), \end{align*}$  and  $\begin{align*}C’ (-4, -5).\end{align*}$
::答复:A_B_C}形状将位于A_(-1,-8,)B_(2,-7)和C_(-4,-5)之间。

Use the interactive below to practice sequences involving all of the rigid motions learned thus far.
::使用以下互动方式,对迄今所了解的所有僵硬动议进行顺序操作。

Sequences of Rigid Motions in Video Games
::视频游戏中固定动作序列

Now you've  finally learned the skills necessary to design your future hit video game! Use the interactive below to explore the finished product.
::现在你终于学会了设计未来打击视频游戏的必要技能了! 使用下面的交互式游戏来探索成品。