Transformations HW 2
Geometry
Name ____________________________
Date ______________ Block ________
1. On the accompanying set of axes,
graph ∆ABC with coordinates A(–1,2),
B(0,6), and C(5,4). Then graph ∆A′B′C′,
the image of ∆ABC after a dilation of 2.
2. When the point (2,-5) is reflected in the x-axis, what are the coordinates of its image?
(1) (-5,2)
(3) (2,5)
(2) (-2,5)
(4) (5,2)
3. Point (-2, 3) is reflected in the x-axis. In which quadrant does its image lie?
(1) I
(3) III
(2) II
(4) IV
4. In the accompanying figure, point P is the center of the square.
Find the image of each of the indicated letters under the given notation.
a) RP ,90 (W )
b) RP ,180 ( Z )
c) RP ,270 ( X )
d) RP ,−90 (Y )
5. The parabola shown in the accompanying diagram undergoes a
reflection in the y-axis.
What will be the coordinates of the vertex after the reflection?
(1) (3,-1)
(3) (-3,1)
(2) (3,1)
(4) (-3,-1)
6. On the accompanying grid, graph
and label quadrilateral ABCD, whose
coordinates are A(-l,3), B(2,0), C(2,-l),
and D(-3,-l). Graph, label, and state
the coordinates of A'B'C'D', the image
of ABCD under a dilation of 2, where
the center of dilation is the origin.
7. In the graph below, the shaded region represents set A of
all points (x,y) such that x 2 + y 2 ≤ 1. The transformation T maps
point (x, y) to point (2x, 4y). Which graph to the right
shows the mapping of set A by the transformation T?
8. What is the image of point (-3,7) after a reflection in the x-axis?
(1) (3,7)
(3) (3,-7)
(2) (-3,-7)
(4) (7,-3)
9. Matthew is a fan of the Air Force’s Thunderbirds flying team and
is designing a jacket patch for the team, as shown in the accompanying
diagram.
If P has the coordinates (a,b), what are the coordinates of Q, the
reflection of P in the line y = x?
(1) (a,b)
(3) (-a,b)
(2) (b,a)
(4) (y,x)
10. A design was constructed by using two rectangles ABDC
and A’B’D’C’. Rectangle A’B’D’C’ is the result of a
translation of rectangle ABDC. The table of translations
is shown below. Find the coordinates of points B and D’.
11. In the accompanying graph, if point P has coordinates (a,b),
which point has coordinates (–b,a)?
(1) A
(2) B
(3) C
(4) D
12. In the accompanying diagram of square ABCD, F is the midpoint
of AB, G is the midpoint of BC, H is the midpoint of CD , and
E is the midpoint of DA.
Find the image of ΔEOA after it is reflected in line A. Is this
isometry direct or opposite? Explain your answer.
13. Triangle ABC has coordinates A(2,0), B(l,7),
and C(5,l). On the accompanying set of axes,
graph, label, and state the coordinates of ΔA' B' C ' ,
the reflection of ΔABC in the y-axis.
14. If x = –3 and y = 2, which point on the accompanying graph
represents (–x,–y)?
(1) P
(3) R
(2) Q
(4) S
15. A function, f, is defined by the set {(2,3), (4,7), (-1,5)}. If f is reflected in the line y = x, which
point will be in the reflection?
(1) (5,-1)
(3) (1,-5)
(2) (-5,1)
(4) (-1,5)
16. If point (5,2) is rotated counterclockwise 90° about the origin, its image will be point
(1) (2, 5)
(3) (-2, 5)
(2) (2, -5)
(4) (-5, -2)
17. Carson is a decorator.
He often sketches his room
designs on the coordinate plane.
He has graphed a square table
on his grid so that its corners
are at the coordinates A(2,6),
B(7,8), C(9,3), and D(4,l). To
graph a second identical table,
he reflects ABCD over the
y-axis. On the accompanying
set of coordinate axes, sketch
and label ABCD and its image
A'B'C'D', which show the
locations of the two tables.
Then find the number of
square units in the area of ABCD.
18. If x = –2 and y = –1, which point on the accompanying
set of axes represents the translation (x,y) → (x + 2, y - 3) ?
(1) Q
(2) R
(3) S
(4) T
19. What are the coordinates of point P, the image of point (3,–4) after a reflection in the line y = x?
(1) (3,4)
(3) (4,–3)
(2) (–3,4)
(4) (–4,3)
20. The image of point (-2,3) under translation T is (3,-l). What is the image of point (4,2) under the
same translation?
(1) (-1,6)
(3) (5,4)
(2) (0,7)
(4) (9,-2)
21. The accompanying diagram shows the starting position of the spinner on a board game.
How does this spinner appear after a 270° counterclockwise rotation about point P?
22. Two parabolic arches are to
be built. The equation of the first
arch can be expressed as
y = − x 2 + 9, with a range of
0 ≤ y ≤ 9, and the second arch is
created by the transformation T7,0.
On the accompanying set of axes,
graph the equations of the two
arches. Graph the line of symmetry
formed by the parabola and its
transformation and label it with
the proper equation.
23. Which of the following rotations about the origin is not equivalent to the other three?
(1) 90 counterclockwise
(3) -270
(2) 270 clockwise
(4) -90
24. Which transformation is not an isometry?
(1) ( x, y ) → ( x + 6, y − 2)
(3) ( x, y ) → ( y, −x )
1
2
(2) ( x, y ) → ( x,
1
y)
2
(4) ( x, y ) → ( − y, −x)
25. Which property is not preserved by a glide reflection?
(1) betweeness
(3) orientation
(2) angle measure
(4) collinearity
26. A line reflection preserves
(1) distance and orientation
(2) angle measurement and orientation
(3) distance, but not angle measurement
(4) distance and angle measurement
27. Given: Triangle ABC with A(2, 3), B(0, 6), and C(2,6). Graph and state the coordinates of:
a. + A ' B ' C ' , the image of + ABC after ry-axis.
b. + A '' B '' C '' , the image of + A ' B ' C ' after ry=x.
c. + A ''' B ''' C ''' , the image of + A '' B '' C '' after RO,90