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In this lesson, we will learn how to apply the concept of translation to a point or a geometric shape and determine the coordinates of a translated image on the xy-plane.

Q1:

The point ( 3 , 5 ) has been translated three right and three down. What are the coordinates of the image?

Q2:

Start with point π΄ ( β 5 , β 1 ) . Translate it by 5 units to the left and 2 units up. Follow this with a translation of 5 units to the right and 4 units up. What are the new coordinates?

Q3:

Determine the coordinates of the image of point π΅ of quadrilateral π΄ π΅ πΆ π· after a translation 5 units left and 3 units down.

Q4:

Write the translation that takes point π΄ to point π΄ β² .

Q5:

Find the image of a β³ π΄ π΅ πΆ , where the coordinates of π΄ , π΅ , and πΆ are ( β 7 , β 7 ) , ( 4 , β 7 ) , and ( 2 , 1 ) , respectively, under the translation ( 3 , 2 ) .

Q6:

Find the coordinates of the point ( π₯ , π¦ ) after it is translated π units left and π units down.

Q7:

If triangle π is mapped to triangle π β² by a translation, would the corresponding angles and sides in the triangle be equal?

Q8:

The vertices of a triangle are mapped using the function ( π₯ , π¦ ) β ( π₯ β 2 , π¦ + 3 ) . Which of the following single transformations has taken place?

Q9:

What is the translation that will move point π΅ to point π΄ ?

Q10:

A figure has been translated three right and two down and then translated a further eight right and six up. What single transformation could have been used?

Q11:

What is the name of the transformation that slides figures without flipping or rotating them?

Q12:

If a point with coordinates ( π₯ , π¦ ) is translated three right and two down, determine the coordinates of the image.

Q13:

What translation moves point π΄ to point π΅ ?

Q14:

Find the coordinates of the point ( π₯ , π¦ ) after it is translated π units right and π units up.

Q15:

Farida wants to change the location of her right-triangular desk. If she moves it only by a translation, will it fit exactly into one of the other corners of the room?

Q16:

A translation maps a point two right and four down. Which of the following functions represents this transformation applied to a general point ( π₯ , π¦ ) ?

Q17:

In the given figure, π΄ has been translated to π΅ . What function would describe this transformation?

Q18:

The points ( 8 , 1 2 ) , ( 1 0 , 7 ) , ( 1 3 , 1 4 ) , ( 1 5 , 9 ) are moved down by 7 units. What are the new coordinates?

Q19:

The coordinates of point π΄ and its image π΄ β² after a translation are illustrated in the graph below. Describe this translation in words.

Q20:

Determine the image of the two points π΄ ( β 2 , β 6 ) and π΅ ( 3 , β 7 ) under the translation ( 3 , 3 ) .

Q21:

Find the images of the points π΄ and π΅ of the line segment π΄ π΅ under the translation ( 4 , 3 ) .

Q22:

In the figure below, determine the coordinates of the points π΄ β² , π΅ β² , πΆ β² , and π· β² , where π΄ β² π΅ β² πΆ β² π· β² is a translation of π΄ π΅ πΆ π· by ( β 2 , β 5 ) .

Q23:

Find the coordinates of the image of ( 1 3 , 4 ) under the translation ( π₯ , π¦ ) β ( π₯ + 5 , π¦ β 2 ) .

Q24:

Given that the translation of point π΄ by ( β 9 , 7 ) is π΄ β² ( β 1 , 2 ) , find the coordinates of π΄ .

Q25:

Find the image of the point π΄ ( β 7 , 1 2 ) under a translation of 13 units in the negative direction of the π₯ -axis.

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