In this lesson, we will learn how to identify an image after a series of transformations and identify a transformation that is the same as a series of transformations.

Q1:

Reflect Triangle π΄ in the π¦ -axis and then in the π₯ -axis. Which triangle is its image?

Q2:

Reflect Triangle π΅ in the π¦ -axis and then in the π₯ -axis. Which triangle is its image?

Q3:

In the given figure, triangle π΄ has been transformed to triangle π΄ β² by reflecting first in the π¦ -axis and then reflecting in the π₯ axis. What single transformation would have mapped π΄ to π΄ β² ?

Q4:

π΄ π΅ πΆ π· is reflected in the π₯ -axis and then translated 5 units to the right. What is the image of point π΅ ?

Q5:

π΄ π΅ πΆ π· is reflected in the π¦ -axis and then translated 2 units to the right. What is the image of point π· ?

Q6:

Does there exist a series of similarity transformations that would map quadrilateral π΄ π΅ πΆ π· to quadrilateral π» πΊ πΉ πΈ ? If yes, explain your answer.

Q7:

In the given figure, what combination of transformations would map circle π΄ onto circle π΅ ?

Q8:

Q9:

Does there exist a series of similarity transformations that would map triangle π΄ π΅ πΆ to triangle πΈ πΉ π· ? If yes, explain your answer.

Q10:

Find the image of point ( β 1 0 , β 9 ) after translation by ( π₯ , π¦ ) β ( π₯ β 8 , π¦ + 5 ) followed by a rotation about the origin through an angle of 9 0 β .

Q11:

Find the image of point ( β 6 , β 4 ) after translation by ( π₯ , π¦ ) β ( π₯ + 8 , π¦ β 4 ) followed by a rotation about the origin through an angle of 9 0 β .

Q12:

Find the image of point ( 9 , 1 ) after translation by ( π₯ , π¦ ) β ( π₯ , π¦ β 4 ) followed by a rotation about the origin through an angle of 9 0 β .

Q13:

The triangle with vertices ( 3 , 3 ) , ( 7 , 0 ) , and ( 1 0 , 5 ) was transformed to ( 1 , 8 ) , ( 5 , 5 ) , and ( 8 , 1 0 ) and then to ( 1 , 8 ) , ( β 2 , 4 ) , and ( 3 , 1 ) . Which of the following describes these transformations?

Q14:

The triangle with vertices ( 3 , 1 ) , ( 1 , 4 ) , and ( 0 , 0 ) was transformed to ( 8 , β 1 ) , ( 6 , 2 ) , and ( 5 , β 2 ) and then to ( 8 , β 1 ) , ( 1 0 , β 4 ) , and ( 1 1 , 0 ) . Which of the following describes these transformations?

Q15:

A transformation maps point π΄ to point π΅ . We say that π΅ is the of π΄ .

Q16:

A transformation maps point π΄ to point π΅ . We say that π΄ is the of π΅ .

Q17:

Triangle π΄ π΅ πΆ can be reflected and then translated onto π· πΈ πΉ .

Determine the length of π΅ πΆ .

Determine the measure of angle π· πΉ πΈ .

Q18:

Which of the following statements will be true for two triangles that are similar.

Q19:

The triangles π΄ π΅ πΆ and π΄ β² π΅ β² πΆ β² in the figure are similar. Which of the following statements justifies this?

Q20:

The quadrilateral π΄ π΅ πΆ π· has been transformed onto quadrilateral π΄ π΅ πΆ π· β² β² β² β² which has then been transformed onto quadrilateral π΄ π΅ πΆ π· β² β² β² β² β² β² β² β² .

Describe the single transformation that maps π΄ π΅ πΆ π· onto π΄ β² π΅ β² πΆ β² π· β² .

Describe the single transformation that maps π΄ β² π΅ β² πΆ β² π· β² onto π΄ β² β² π΅ β² β² πΆ β² β² π· β² β² .

Hence, are quadrilaterals π΄ π΅ πΆ π· and π΄ β² β² π΅ β² β² πΆ β² β² π· β² β² similar?

Q21:

The triangle π΄ π΅ πΆ has been transformed onto triangle π΄ π΅ πΆ β² β² β² which has then been transformed onto triangle π΄ π΅ πΆ β² β² β² β² β² β² .

Describe the single transformation that maps π΄ π΅ πΆ onto π΄ β² π΅ β² πΆ β² .

Describe the single transformation that maps π΄ β² π΅ β² πΆ β² onto π΄ β² β² π΅ β² β² πΆ β² β² .

Hence, are triangles π΄ π΅ πΆ and π΄ β² β² π΅ β² β² πΆ β² β² similar?

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