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.
Translating points
Source: Khan Academy, https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-translations/v/translating-points This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.
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: