Honors Geometry Unit 1 Transformations in the Coordinate Plane Test Review
I. Find the coordinates of the reflection without using a coordinate plane.
1. L (2,3) reflected in the x-axis 2. M(-2, -4) reflected in the line x
=2
3. N (-4, 0) reflected in the line 4. P (8.2, -3) reflected in y-axis
y=x
II. Draw ∆PQR, ∆P’Q’R’, and ∆P” Q”R” using the given transformations in the order
they appear.
5. P (5, 1), Q (3, 4), R (0, 1) 6. P (7, 2), Q (3, 1), R (6, -1)
Translation: (x, y)→(x-2, y-4) Translation: (x, y)→(x-4, y+3)
Reflection: in the y-axis Rotation: 90° clockwise about
the origin
III. Write a rule for the translation.
7. 1 unit to the left and 1 unit up 8. 3 units down
9. 7 units to the left and 4 units 10. 10 units right and 8 units up
down
IV. Rotations
11. Suppose ∆ABC has vertices A(-8, -2), B (-5, -2), and C (-8, -7). If ∆ABC is rotated
90° counterclockwise about the origin, what are the coordinates of the vertices
of ∆A’B’C’?
V. Vocabulary
Image Isometry Pre-image Reflection
Rotation Transformation Translation
Use only the words in the above to fill in the blanks below.
12. _______________ A transformation of a figure that creates a mirror image over
a line.
13. _______________ A transformation that slides each point of a figure the same
distance in the same direction.
14. _______________ The mapping, or movement, of all points of a figure in a plane
according to a common operation.
15. _______________ A figure before a transformation has taken place.
16. _______________ A distance preserving map of a geometric figure to another
location using a reflection, rotation, or translation.
17. _______________ The result of a transformation.
Determine whether the figure has rotational symmetry. If so, state the rotations that map
the figure onto itself.
18. 19. 20.
Rotational Symmetry? Rotational Symmetry? Rotational Symmetry?
_____ _____ _____
If yes, state the degree If yes, state the degree If yes, state the degree
of rotation: of rotation: of rotation:
Draw all lines of symmetry.
21. 22.
Draw a figure for the description. If not possible, write “not possible”.
23. A trapezoid with exactly one line of 24. A triangle with exactly two lines of
symmetry. symmetry.
In the diagram, lines r and s are parallel.
25. A translation maps CD onto which segment
26. Is the distance from C to r the same as the
distance from C′ to r Explain.
27. Use the translation (x, y) → (x + 1, y - 7) to answer each question below.
a. What is the translation vector? __________
b. What is the image of A (10, -4)? __________
c. What is the image of A’ from part b, which would be called A”? __________
d. What is the pre-image of C’ (-9, 12)? __________
28. Given ∆ABC with A(-1, 0), B(5, 3), and C(2, -4), find the vertices of ∆A’B’C’ given the
transformation rules below. Then determine the type of transformation which occurred.
a. (x, y) → (x + 11, y – 5) A’ = __________ B’ = __________ C’ = __________
Transformation: _____________________________
b. (x, y) → (-x, -y) A’ = __________ B’ = __________ C’ = __________
Transformation: _____________________________
c. (x, y) → (y, -x) A’ = __________ B’ = _________ C’ = __________
Transformation: _____________________________
d. (x, y) → (y, x) A’ = __________ B’ = __________ C’ = __________
Transformation: _____________________________
e. (x, y) → (-y, x) A’ = __________ B’ = __________ C’ = __________
Transformation: ____________________________
Write the transformation rule for the following graphs.
29. _________________ 30. _________________
Follow the instructions for each graph.
31. Reflection across y = -x. 32. Rotation 90° CCW
33. <2, 3> 34. (x, y) → (x, y – 4)
Composition of Transformations
Remember to label/name the first transformation with ∆A’B’C’, the second transformation with
∆A”B”C”.
35. a. Rotation 180° 36. a. reflection across y = x.
b. reflection over y = -1 b. Rotation 90°CW
A’ ________ A” ________ A’ ________ A” ________
B’ ________ B” ________ B’ ________ B” ________
C’ ________ C” ________ C’ ________ C” ________
