# Transformations Level 6

## Learn how to solve mixed transformation problems and answer exam-style questions.

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This is level 6: mixed questions without diagrams. You can earn a trophy if you get at least 9 questions correct and you do this activity online.

If the answer to a question is a pair of coordinates, you need to type in the brackets and comma like this $$(2,3)$$

 1. What are the coordinates of the point $$(3,4)$$ after it has been translated by the vector $$\begin{pmatrix} 1 \\ 3 \\ \end{pmatrix}$$ ? 2. What are the coordinates of the point $$(2,2)$$ after it has been translated by the vector $$\begin{pmatrix} -3 \\ -4 \\ \end{pmatrix}$$ ? 3. What are the coordinates of the point $$(3,1)$$ after it has been reflected in the line $$y = x + 3$$ ? 4. What are the coordinates of the point $$(1,-3)$$ after it has been reflected in the line $$y = 6 - x$$ ? 5. What are the coordinates of the point $$(2,-6)$$ after it has been rotated through an angle of $$180^{\circ}$$ about the point $$(-3,6)$$ ? 6. What are the coordinates of the point $$(3,0)$$ after it has been rotated through an angle of $$90^{\circ}$$ anticlockwise about the point $$(-1,-6)$$ ? 7. What are the coordinates of the point $$(4,5)$$ after an enlargement of scale factor $$2$$ with centre of enlargement at $$(0,2)$$ ? 8. What are the coordinates of the point $$(-5,-3)$$ after an enlargement of scale factor $$3$$ with centre of enlargement at $$(-5,-6)$$ ? 9. What are the coordinates of the point $$(-3,5)$$ after it has been reflected in the line $$x = 1$$ and then rotated through $$180^{\circ}$$ about $$(3,-2)$$ ? 10. What are the coordinates of the point $$(4,-5)$$ after it has been translated by the vector $$\begin{pmatrix} -5 \\ -6 \\ \end{pmatrix}$$ then enlarged with a scale factor $$5$$ and a centre of enlargement at $$(-2,-3)$$ ? 11. What are the coordinates of the point $$(-5,-5)$$ after an enlargement of scale factor $$4$$ with centre of enlargement at $$(5,-1)$$ followed by a reflection in the line $$y = 2$$ ? 12. What are the coordinates of the point $$(-6,4)$$ after it has been rotated through an angle of $$90^{\circ}$$ anticlockwise about the point $$(-1,0)$$ followed by being translated by the vector $$\begin{pmatrix} 2 \\ 1 \\ \end{pmatrix}$$ followed by an enlargement of scale factor $$3$$ with centre of enlargement at $$(-5,-4)$$ ?
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This is Transformations level 6. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 7

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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## Teachers

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## Description of Levels

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Level 1 - Reflect a shape in a given line

Level 2 - Translate a shape by a given vector

Level 3 - Rotate a shape about a given point by a given angle

Level 4 - Enlarge a shape from a given point by a given scale factor

Level 5 - Transform a shape by a given matrix

Level 6 - Mixed questions without diagrams

Level 7 - Describe the transformation from the diagrams

Exam Style questions are in the style of GCSE or IB/A-level exam paper questions and worked solutions are available for Transum subscribers.

There is a printable worksheet to go with this activity.

Finally try Blow Up, a clallenge to find all the points that could be the centre of enlargement of a shape if the image does not go off the grid. Great fun!

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Help

You may want to open the Graph Plotter in a new tab to help you answer these questions.

Alternatively you could print some Graph Paper, have it laminated then use a non-permanent pen as a handy working resource.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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