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Use the given translation to find the coordinates of the image of quadrilateral ABCD****.
1.
x y , x 4 , y 5 2.
x y , x 2 , y 3
Write a rule for the translation of the preimage to the image.
3 4.
Graph the polygon with the given vertices and its image after a rotation of the given number of degrees
clockwise about the origin.
5.
4, 1 , 4, 4 , 1, 4 , 1, 3 ;
180
A B C D
6.
D 3, 5 , E 4, 1 , F 1, 1 ; 90
Determine whether the polygons with the given vertices are congruent, similar or neither. Use transformations
to explain your reasoning.
7.
A 6, 3 , B 3, 7 , C 2, 5 and E 7, 1 , F 4, 9 , G 1, 7
8. 𝑊
( 0 , − 1
) , 𝑋
( − 5 , − 1
) , 𝑌
( − 3 , 2
) , 𝑍
( − 1 , 2
) and 𝐾
( 0 , − 1
) , 𝐿
( 5 , 2
) , 𝑀
( 3 , 4
) , 𝑁( 1 , 4 )
Determine whether the object has line symmetry and whether it has rotational symmetry. Identify all lines of symmetry
and angles of rotation that map the figure into itself.
9. 10. 11.
Geometry Chapter 4 Review
Describe a congruence transformation that maps the black preimage to the grey image.
12. 13. 14. Consider triangle ABC with vertices
A 0, 0 , B 0, 4 , C 6, 0 .The image
of triangle ABC after a dilation has vertices
A 0, 0 , B 0, 10 , C 15, 0 .What is the scale factor of
the dilation?
15. Triangle ABC with vertices
A 2, 5 , B 1, 8 , C 7, 5 is dilated using a
scale factor of
1
2
3 .What are the coordinates of the image of triangle ABC?
Describe a similarity transformation that maps the first polygon to the second polygon.
16.
6, 6 , 6, 3 , 3, 3 , 3, 6 and 2, 2 , 2, 1 ,
1, 1 , 1, 2
A B C D J K
L M
17.
A 1, 2 , B 2, 2 , C 1, 4 and D 4, 6 , E 6, 6 , F 4, 2
In Exercises 1 8 and 19 , graph ∆𝑷𝑸𝑹 with vertices
P 1, 5 , Q 4, 3 , and R 2, 1
and its image after the similarity transformation.
18. Rotation: 180 about the origin 19. Dilation:
1 1
2 2
x y , x , y
Dilation:
x y , 2 , 2 x y Reflection: in the x - axis
In Exercises 20 and 2 1 , find the scale factor of the dilation. Then tell whether the
dilation is a reduction or an enlargement****.
