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Translations: Writing the Rule – Understanding transformations – Transformations change a shape’s position or size. – Congruence and translations – Translated shapes remain congruent to the original. – Translations as slides – Imagine sliding a shape without rotating or flipping it. – Writing translation rules – Use (x, y) ’ (x+a, y+b) to denote translation. | This slide introduces the concept of transformations in geometry, focusing on translations. Students will learn that transformations can alter a shape’s position or size, but translations specifically slide shapes without rotation or flipping, maintaining congruence. Congruence implies that the size and shape are preserved. The objective is to understand and write the rule for translations, which is expressed as moving every point of a shape a fixed distance in a given direction. The rule for translations can be written in coordinate form as (x, y) ’ (x+a, y+b), where ‘a’ and ‘b’ are the horizontal and vertical distances the shape is moved, respectively. Encourage students to practice writing translation rules for various shapes and distances to solidify their understanding.

Understanding Translations in Geometry – Translation: sliding a shape – A translation moves a shape in a straight path without rotation. – Shapes stay congruent – Congruent: identical in shape and size after the move. – Orientation is preserved – The shape keeps the same direction, no turns or flips. – Chess piece: real-life example – Moving a rook vertically or horizontally on the board. | This slide introduces the concept of translation in the context of geometric transformations. Emphasize that a translation is a type of transformation that slides a shape in any direction but does not change its size, shape, or orientation. Use the chess piece example to illustrate a real-world application of translation, where a rook moves in a straight line without turning. This helps students visualize the concept. Discuss how the properties of congruence and orientation are important in understanding that the shape remains the same before and after the translation. Encourage students to think of other examples of translations they might encounter in everyday life.

Translation Rules in Coordinate Geometry – Understand translation notation – T(x, y) ’ (x+a, y+b) shows how points shift on a graph. – Horizontal translations explained – Moving left or right changes the x-coordinate. – Vertical translations clarified – Moving up or down alters the y-coordinate. – Writing rules for translations – Use the notation to describe shifts in positions. | This slide introduces students to the concept of translations in the context of coordinate geometry. The translation notation T(x, y) ’ (x+a, y+b) is a formal way of representing how each point in a shape moves in a coordinate plane. Horizontal translations involve adding or subtracting from the x-coordinate, which moves the shape left or right. Vertical translations involve the y-coordinate, moving the shape up or down. Students should learn to apply this notation to write rules that describe how to translate a figure on a graph. Encourage students to practice by picking points and applying different values of ‘a’ and ‘b’ to see how the points move. This will help them visualize the translation process and understand the effects of different translation vectors.

Translations: Horizontal and Vertical – Horizontal translation rule – T(x, y) ’ (x+5, y) shifts a point 5 units right – Vertical translation rule – T(x, y) ’ (x, y-3) shifts a point 3 units down – Combining translations – To move a shape, apply both horizontal and vertical rules – Practical application of rules – Use these rules to graph translations on a coordinate plane | This slide introduces students to the concept of translations in the coordinate plane. A horizontal translation moves a shape or point to the left or right, while a vertical translation moves it up or down. When given a rule like T(x, y) ’ (x+5, y), it indicates a shift of 5 units to the right. Conversely, T(x, y) ’ (x, y-3) represents a downward shift of 3 units. Students should understand that these translations can be combined to move a shape in two directions simultaneously. Encourage students to practice by applying these rules to different shapes on graph paper, reinforcing the concept through visual learning. This will help them visualize how shapes are transformed on a coordinate plane and understand the underlying principles of translations in geometry.

Let’s Practice Writing Translation Rules! – Translate triangle 4 units up – (x, y) -> (x, y + 4) – Translate square 2 units left – (x, y) -> (x – 2, y) – Translate circle right and down – (x, y) -> (x + 3, y – 5) – Writing the rule for translations | This slide is designed to help students practice writing rules for translating shapes on the coordinate plane. Start with a simple translation of a triangle 4 units up, which can be expressed as moving every point of the triangle from (x, y) to (x, y + 4). For the square, translate it 2 units to the left, which is written as (x, y) to (x – 2, y). The circle’s translation is a bit more complex, moving 3 units to the right and 5 units down, resulting in the rule (x, y) to (x + 3, y – 5). Encourage students to visualize these movements on a graph and to write the general rule for translations: (x, y) to (x + a, y + b), where ‘a’ and ‘b’ are the horizontal and vertical shifts, respectively. Have students practice with additional shapes and translations to solidify their understanding.

Class Activity: Create Your Translation! – Select a shape and plot on grid – Choose a direction to translate – Write the translation rule – Rule format: (x, y) -> (x+a, y+b) – Share your translation | This activity is designed to help students understand the concept of translations in a fun and interactive way. Students will first choose any shape they like and plot it on a coordinate grid. Then, they will decide in which direction they want to translate their shape: up, down, left, or right. They will write down the rule for their translation, which involves adding or subtracting from the x and y coordinates. For example, moving a shape 3 units to the right involves adding 3 to the x-coordinate (x, y) -> (x+3, y). After applying this rule to their shape, students will share their original shape and its translation with the class. This will help them see how the rule applies and how the shape’s position changes on the grid. Provide guidance on how to write the rule and encourage creativity in their shape selection and translation choices.

Translations: Review and Reflect – Recap of translation concept – Translations slide figures without rotating or resizing them. – Writing translation rules – Use notation (x, y) ’ (x+a, y+b) to denote a shift. – Significance of understanding translations – Grasping translations aids in geometry problem-solving and understanding shapes’ movement. | Today’s lesson focused on understanding translations in the context of geometric transformations. We learned that a translation is a type of transformation that slides a figure on the coordinate plane without rotating or resizing it. When writing a translation rule, we use the notation (x, y) ’ (x+a, y+b), where ‘a’ and ‘b’ represent the horizontal and vertical shifts, respectively. Understanding translations is crucial as it forms the basis for more complex geometric concepts and is widely applicable in various real-world scenarios, such as in engineering and computer graphics. Encourage students to reflect on how this concept connects to previous knowledge and how it might be used in future mathematical applications.

Homework Challenge: Exploring Translations – Find an object to translate – Write the object’s translation rule – Describe the movement in terms of direction and distance – Understand the translation process – How does translation affect an object’s position without altering its shape? – Discuss your findings in class | This homework challenge is designed to help students apply the concept of translations to real-world objects. Students should select any object at home and then describe how to translate it from one position to another using a rule. The rule should include the direction and distance of the movement, such as ‘move 5 units right and 3 units up’. Encourage students to think about how the object’s position changes while its shape remains the same. In the next class, students will share their objects and translation rules, fostering a discussion on the practical application of translations in everyday life. This activity will reinforce their understanding of the concept and how to express translations mathematically.