Translations

Site: Saylor Academy
Course: GKT101: General Knowledge for Teachers – Math
Book: Translations
Printed by: Guest user
Date: Wednesday, May 14, 2025, 2:03 PM

Description

Translation is a type of rigid transformation. Watch this lecture series and complete the interactive exercises.

Determining translations

Translating shapes

Translation challenge problem

Practice

    

Translate points - Questions

1. Plot the image of point \(Q\) under the translation \((x, y) \rightarrow(x+1, y+2)\).



2. Plot the image of point \(P\) under a translation by 5 units to the right and 7 units down.



3. Point \(P^{\prime}\) is the image of \(P(5,-5)\) under a translation by 2 units to the left and 5 units up.

What are the coordinates of \(P^{\prime}\)?

(_________, _________)


4. Point \(P^{\prime}\) is the image of \(P(6,0)\) under the translation \((x, y) \rightarrow(x-6, y-1)\).

What are the coordinates of \(P^{\prime} ?\)

(_________, _________)



Translate points - Answers

1. The image \(Q^{\prime}\) of point \(Q\) is at the coordinates \((-3,6)\).


2. The image \(P^{\prime}\) of point \(P\) is at the coordinates \((4,-2)\).



3. The coordinates of \(P^{\prime}\) are \((3,0)\).

4. The coordinates of \(P^{\prime}\) are \((0,-1)\).

Determine translations - Questions

1. 


Determine the translation.

Use non-negative numbers.

A translation by _______ units to the _______  (right/left) and _______  units _______  (up/down).

2. Quadrilateral \(A^{\prime} B^{\prime} C^{\prime} D^{\prime}\) is the image of quadrilateral \(A B C D\) under a translation by 2 units to the right and 5 units down.



Point \(B^{\prime}(6,-5)\) is the image of \(B(-5,-2)\) under a translation.

Determine the translation.

Use non-negative numbers.

A translation by _______ units to the _______  (right/left) _______  and units _______  (up/down).

3. \(\triangle A^{\prime} B^{\prime} C^{\prime}\) is the image of \(\triangle A B C\) under a translation.

Determine the translation.

Use non-negative numbers.

A translation by _______ units to the _______  (right/left) _______  and units _______  (up/down).

4. Point \(D^{\prime}(7,1)\) is the image of \(D(7,6)\) under a translation.

Determine the translation.

Use non-negative numbers.

A translation by _______ units ________(right/left/up/down)


Determine translations - Answers

1. A translation by 2 units to the right and 5 units down.

2. \(B^{\prime}\) is the image of \(B\) under a translation by 11 units to the right and 3 units down.


3. \(\triangle A^{\prime} B^{\prime} C^{\prime}\) is the image of \(\triangle A B C\) under a translation by 4 units to the right and 2 units up.


4. \(D^{\prime}\) is the image of \(D\) under a translation by 5 units down.


Translate shapes - Questions

1. Draw the image of \(\triangle A B C\) under the translation \((x, y) \rightarrow(x+2, y+2)\).



2. Draw the image of quadrilateral \(A B C D\) under a translation by 1 unit to the right and 4 units up.


3. Draw the image of \(\triangle A B C\) under the translation \((x, y) \rightarrow(x, y+3)\).



4. Draw the image of \(\triangle A B C\) under a translation by 1 unit to the left and 5 units up.


Translate shapes - Answers

1. Doing this for all vertices and connecting them, we get the following mapping:



2. Doing this for all vertices and connecting them, we get the following mapping:


3. Doing this for all vertices and connecting them, we get the following mapping:



4. Doing this for all vertices and connecting them, we get the following mapping: