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WorksheetsConstructions and Transformations Practice Test
Total questions: 115
Worksheet time: 2hrs 4mins
The drawing shows a compass and straight edge construction of...what?
the bisector of a given angle
a perpendicular to a given line at a point on the line
a perpendicular to a given line from a point NOT on the line
an angle congruent to a given angle
the midpoint of a big angle
The given diagram is what kind of construction?
Perpendicular bisector
Congruent angles
Angle bisector
Congruent line segments
Similar Angles
When copying line segment AB using a straight edge and a compass, the compass should be used to:
Draw an arc above point A
Measure the length of segment AB
Draw an arc between point A and point B
Measure half the length of line segment AB
To create a double fish to be the perpendicular line to segment AB
What is being constructed in the figure?
the perpendicular bisector of line m
the line perpendicular to line m through a point on the line
the line parallel to line m through a point NOT on the line
an angle that has line m as its bisector
angle p is bisected through line m creating an angle bisector that is parallel to the line
When constructing a line parallel to a given line, you will be
copying a segment
bisecting a segment
copying an angle
constructing a perpendicular
bisecting an angle
What type of construction do you see?
congruent segments
angle bisector
perpendicular bisector
altitude
median
Name the construction.
midpoint
perpendicular through a point on the line
perpendicular through a point NOT on the line
circumcenter of a right triangle
perpendicular bisector
The drawing shows the arcs used to construct...what?
a bisector of a given line
a bisector of a given angle
a perpendicular of a given line at a point on the line
an angle congruent to a given angle
creating parallel lines given an angle
What type of construction is illustrated in the diagram?
Angle congruent to angle D
Line segment congruent to AD
Angle congruent to angle D
Bisection of angle D
Creating the long diagonal of trapezoid ABCD
What does the word BISECT mean?
To cut something into more than five pieces.
It is a insect with two sets of wings.
A shape that has three sides.
To cut something into two congruent pieces or in half.
To create and angle equal to 90 degrees
An angle that measures exactly 90°
Acute Angle
Right Angle
Triangle
Straight Angle
Oblique Angle
Which of the following constructions is illustrated?
An angle is congruent to a given angle
The bisector of a given angle
The bisector of a given segment
The perpendicular bisector of a given segment.
Coping a given adjacent angle.
Name the construction.
Angle bisector
Perpendicular line to a point not on a line
Perpendicular line to a point on the line
Perpendicular bisector of a line segment
Creating congruent segments
Name the construction.
Angle bisector
Perpendicular line to a point not on a line
Angle median
Perpendicular bisector of a line segment
Creating congruent angles
Name the construction.
Parallel line to a point not on the line using alternate interior angles
Parallel line to a point not on the line using corresponding angles
Perpendicular line to a point not on the line
Angle bisector
Perpendicular Bisector
Name the construction.
Angle bisector
Di-sect an angle
Copy an angle
Vertical angles
Bisect an angle
What type of construction do you see?
midpoint
angle bisector
perpendicular bisector
altitude
median
Which one is the correct construction for a perpendicular bisector?
1
2
3
4
None of the above
Marsha is using a straightedge and compass to do the construction shown. Which best describes the construction Marsha is doing?
a line through P parallel to line l
a line through P intersecting line l
a line through P congruent to line l
a line through P perpendicular to line l
a line through P creating a transversal through line l
Based on the construction, which conclusion is not always true?
A
B
C
D
All Statements on the bottom are true!
Identify the transformation from ABCD to A'B'C'D'.
Translation <2,0>
Reflection across the x-axis
Reflection across the y-axis
90o counter clockwise rotation
Translation <-2,0>
Identify the transformation from ABC to A'B'C'.
(x+8, y+4)
(x-8, y-4)
(x+4, y+8)
(x-4, y-8)
None of the above
Identify the transformation from ABC to A'B'C'.
90o clockwise rotation
90o counter clockwise rotation
Reflection across the y-axis
Reflection across the x-axis
Translation (x, y-2)
Identify the transformation from ABCD to A'B'C'D'.
Translation (x-7,y)
Reflection across the y-axis
Reflection across the x-axis
90o counter clockwise Rotation
Translation (x+7,y)
Which rule would result in a clockwise rotation of 90° about the origin?
(x, y) → (y, -x)
(x, y) → (y,x)
(x, y) → (x, -y)
(x, y) → (-x,-y)
(x, y) → (-y,-x)
Which rule would result in a translation of 2 units left and 3 units up?
(x, y) → (2x, 3y)
(x, y) → (x - 2, y + 3)
(x, y) → (3x, 2y)
(x, y) → (x + 2, y - 3)
(x, y) → (-2x, -3y)
What is the rule for the dilation pictured below?
(x, y) → (½x, ½y)
(x, y) → (x + 2, y + 2)
(x, y) → (x + ½, y + ½)
(x, y) → (2x, 3y)
(x, y) → (2x, 2y)
Identify the transformation from C to D. Check ALL that apply
90o Clockwise Rotation
180o Rotation
270o Clockwise Rotation
270o Counter-Clockwise Rotation
90o Counter-Clockwise Rotation
The point Z(4, -2) is rotated 180 degrees about the origin. What is the image of Z?
Z'(2, 4)
Z'(-4, 2)
Z'(-2, -4)
Z'(-4, -2)
Z'(-2, 4)
An office supply store sells index cards in two different sizes. The large size is an enlargement of the small size. Both sizes are shown. Find the scale factor of the enlargement.
2
3
1/2
1/3
Not enough information
Name the image of C(6, -4) under a rotation 90 degrees counterclockwise about the origin.
C'(4, 6)
C'(-4, -6)
C'(6, 4)
C'(-6, -4)
(-6,4)
Given C(2, 9), under which reflection is C'(-2, 9)?
reflected in the x-axis
reflected in the y-axis
reflected in the line x = 2
reflected in the line y = x
reflected in the line y = -x
Two objects that are the same shape but not the same size are _______.
Congruent
Vertical
Similar
Complementary
Dilation
When you translate, (x+4,y) will move _____.
4 units right
4 units left
4 units up
4 units down
the figures x values are 4x larger
Identify the transformation.
Reflection across y-axis
90 Rotation counter clockwise
Translation 5 units left, 1 unit up.
Translation 5 units right, 1 unit down
Reflection across the y-axis with a translation 3 units right, and 1 unit down.
The point that is to be transformed is called the:
Pre-Image
Image
Post-Image
Transformation
Mapping
What Transformation is visible?
Reflection
Translation
Dilation
Rotation
Expansion
What Transformation is visible?
Reflection
Rotation
Dilation
Translation
Not enough information
How was B translated to B' if B' is at (4, -2)?
Reflected over the y-axis
Translated 2 units to the left and 6 units down
Translated 2 units to the right and 6 units down
Translated 2 units to the right
Reflected over the x-axis
The point (8, 12) was dilated to become point (2, 3). What was the scale factor?
½
¼
4
2
1/6
Square ABCD is reflected about side BC. Which of the following statements are true?
BC is parallel to AA'
Vertex B is the midpoint of AA'.
The length of CD' is twice the length of DD'
Vertex C and C' are located at 2 different points.
CB is parallel to the points of reflections
What is the lowest degree of rotation greater than 0° that will carry the hexagon onto itself?
90 degrees
180 degrees
270 degrees
360 degrees
None of these rotations would create the original hexagon
Which figure when rotated 90 degrees will carry onto itself
square
hexagon
rectangle
triangle
pentagon
Reflect Point C over the y-axis:
(-3, 2)
(3,2)
(-2,3)
(3,0)
(3,-2)
Which pair have a line of reflection of x = -2?
A & B
B & C
G & H
E & F
F & D
Which pair have a line of reflection of x = -3?
A & B
B & C
G & H
E & F
D & F
Which of the following is NOT a reflection?
A & B
B & C
G & H
E & F
A & E
Describe the translation from A to D.
(6, -6)
<6, -6>
<-6, 6)
(x - 6, y + 6)
(x - 6, y - 6)
Identify both ways to translate from B to C.
(4, 0)
<4, 0>
<-4, 0>
(x + 4, y)
(x, y+4)
Describe the transformation from C to H.
translation <2, -10>
rotation 90° CW
rotation 180°
reflection across x-axis
translation <1, -7>
Describe the transformation from E to H. Check all that apply
rotation 270° Counter-Clockwise
rotation 270° Clockwise
rotation 90° Counter-Clockwise
reflection across y-axis
rotation 90° Clockwise
Which of the following describes the sequence of transformations shown?
Reflect across the x-axis and then rotate 90 degrees clockwise around the origin
Rotate 90 degrees clockwise around the origin and then translate down.
Reflect across the x-axis and then reflect across the y-axis.
Translate up and then rotate 90 degrees counter-clockwise about the origin.
Reflect across the x-axis and then rotate 90 degrees counter-clockwise around the origin
(-3, -1) -- Reflect across the line y=x and translate down 1.
(-1, -4)
(-1, -2)
(3, 0)
(-2, -3)
(-1,-3)
(6, -4) -- Dilate by 1/2 and reflect across the origin.
(-3, 2)
(-3, -2)
(12, -8)
(-12, 8)
(2, -3)
Choose the correct transformations
rotate 90 degrees counter-clockwise around the origin, and then reflect over the x-axis
right 1, down 4, and then reflection over the y-axis
right 6, and then reflection over the x-axis
reflection over the line y=x, and then translate up 4, right 2
reflect over the x-axis, and then left 6
Choose the correct transformations
rotate 90 degrees counter-clockwise around the origin, and then reflect over the x-axis
right 1, down 4, and then reflection over the y-axis
right 6, and then reflection over the x-axis
reflection over the line y=x, and then translate up 4, right 2
reflect over the y axis, and then left 1 and up 4
What sequence of transformations will get you from shape BCD to shape B"C"D" in two steps?
Rotation, then Rotation
Rotation, then Dilation
Reflection, then Rotation
Translation, then Reflection
Dilation, then Reflection
Choose the correct transformations
rotate 90 degrees counter-clockwise around the origin, and then reflect over the x-axis
right 1, down 4, and then reflection over the y-axis
right 6, and then reflection over the x-axis
reflection over the line y=x, and then translate up 4, right 2
rotate 90 degrees clockwise around the origin, and then reflect over the y-axis
Name the series of transformations that maps ABC onto DEF
reflect over x then translate left 6 up 1
reflect over y then translate down 6 left 1
translate right 6 down 1, then reflect over x
rotate 90 clockwise then reflect over y
rotate 180 degrees, then left 2 and down 1
(2, 6) -- Translate up 3, left 1 and rotate 180°
(-1, -7)
(1, -7)
(5, 5)
(-5, -5)
(1, -7)
Name the pictured construction.
Circled Hexagon
Hexagon Inscribed in a Circle
Square Inscribed in a Circle
Triangle Inscribed in a Circle
Circumscribed Pentagon
Connecting every other point where the arcs intersect the circle will finish the construction of what polygon?
Inscribed equilateral triangle
Inscribed square
Inscribed hexagon
Circumscribed hexagon
Circumscribed isosceles triangle
The steps shown are a part of the construction of which figure?
inscribed square
circumscribed rectangle
inscribed equilateral triangle
regular hexagon
circumscribed equilateral triangle
A triangle with all sides in equal length is
an obtuse triangle.
a right triangle.
an isosceles triangle.
an equilateral triangle.
an scalene triangle.
Name the construction pictured
Circumscribed Pentagon
Inscribed Square
Circumscribed Triangle
Inscribed Equilateral Triangle
Inscribed Hexagon
A straightedge and compass were used to creat the construction above. Arc EF was drawn from Point B, and arcs with equal radii were drawn from E and F. Choose all of the following that must be true.
Which of the following shows a construction of a 45o angle?
All of the constructions show a 45o angle
Based on the construction above which of the following are always true, choose all that apply.
AB=CD
AE=EB
CE=ED
AC=BC
A line perpendicular to one of two parallel lines is perpendicular to the other.
Two lines are perpendicular if they intersect to form congruent adjacent angles.
When two lines are intersected by a traversal and alternate interior angles are congruent, the lines are parallel.
When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel.
There is not enough done on this construction to prove anything about the two lines.
Which construction of parallel lines is justified by the theorem "If two lines are cut by a transversal to form congruent alternate interior angles, then the lines are parallel"?
not enough information to construct parallel lines
Write a rule for the translation.
(x -1, y + 2)
(x -2, y + 1)
(x +2, y - 1)
(x +1, y - 2)
Not enough information to write a rule.
Identify the transformation from ABC to A'B'C'.
90o clockwise rotation
90o counter clockwise rotation
Reflection across the y-axis
Reflection across the x-axis
Translation down 2 units
Identify the transformation from ABCD to A'B'C'D'.
Translation (x,y) -->(x-7,y)
Reflection across the y-axis
Reflection across the x-axis
90o counter clockwise Rotation
Translation (x,y) --> (x+7, y)
Identify the transformation from A to D.
90o Clockwise Rotation
180o Rotation
270o Clockwise Rotation
Y-Axis Reflection
X-Axis Reflection
Which rule would dilate shows a scale factor of 4
(x, y) → (y, x)
(x, y) → (x + 4, y + 4)
(x, y) → (x - 4, y -4)
(x, y) → (4x, 4y)
(x, y) → (1/4x, 1/4y)
What is the rule for the dilation pictured below?
(x, y) → (½x, ½y)
(x, y) → (x + 2, y + 2)
(x, y) → (2x, 2y)
(x, y) → (2x, 3y)
(x, y) → (1/3x, 1/3y)
A triangle has vertices with coordinates (2,0), (3, -1) and (-2,-5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image?
(5,3), (6,2), (1,-2)
(6,0), (9,-3), (-6,-15)
(2/3,0), (1,-1/3), (-2/3,-5/3)
(-1,-3), (0,-4), (-5,-8)
Not enough information
What is the sequence of transformations?
Reflect over the y then reflect over the x
Reflect over the x then reflect over the y
Translate 4 units then rotate 90˚
Rotate 90˚ then reflect over the x
Rotation of 180 degrees
Which of the following describes the sequence of transformations shown?
Reflect across the x-axis and then rotate -90 (clockwise) around the origin
Rotate -90 (clockwise) degrees around the origin and then translate down.
Reflect across the x-axis and then reflect across the y-axis.
Translate up and then rotate 90 (counterclockwise) degrees about the origin.
Y-Axis reflection and then a x-axis reflection.
What types of transformations happened to get from shape 1 to shape 3, choose ALL that apply.
Rotation
Translation
Reflection
Dilation
Non-Rigid Transformation
Dilate Point B by a scale factor of 1/2
(1.5,-4)
(-1.5,1)
(-1,-1.5)
(-2,-2)
(-6,4)
Choose the correct transformations
rotate 90 degrees counter-clockwise around the origin, and then reflect over the x-axis
right 1, down 4, and then reflection over the y-axis
right 6, and then reflection over the x-axis
reflection over the line y=x, and then translate up 4, right 2
reflection over the y-axis, and then (x,y) --> (x-1, y+4)
Describe the transformations that map ABC onto A"B"C"
translate 5 up and 1 left then reflect over y
translate 5 down and 1 left, then reflect over y
reflect over y=x then translate left 8
reflect over x then rotate 90 clockwise
reflect over the x-axis then translate 4 to the right
Choose the correct scale factor:
2
3
1/3
1/2
Not enough Information
What is an isometry?
A transformation that changes the preimage size.
A transformation that translates the image.
A transformation that preserves the preimage shape and size, such as, a reflection, translation, and rotation.
A transformation that morphs the preimage to a new shape.
What is the rule for the following reflection?
Reflection across y = −2
Reflection across x = −2
Reflection across x = 2
Reflection across y = 2
Reflection across y = x
Identify the smallest angle of rotation that maps the image to itself.
180°
360°
90°
No rotational symmetry
72°
The rule for dilation is
(x, y) --> _
(kx, ky)
(x, -y)
(-x, y)
(x+a, y+b)
(-x,-y)
The rule for reflection over the x-axis is
(x, y) --> _
(-x, y)
(x, -y)
(y, x)
(-y, -x)
(-x,-y)
The rule for rotation of 90 degrees counterclockwise is
(x, y) --> _
(y, -x)
(-y, x)
(x, -y)
(-x, y)
(-x,-y)
The rule for rotation of 180 degrees is
(x, y) --> _
(-y, x)
(-x, -y)
(y, -x)
(-y, -x)
(-x, y)
Which rule describes the action of the coordinates when a figure is reflected over the line y = x?
(x, y)→(-y, -x)
(x, y)→(-x, y)
(x, y)→(-x, -y)
(x, y)→(y, x)
(x, y)→(-y, x)
Which rule describes the action of the coordinates when a figure is reflected over the line y = -x?
(x, y)→(y, x)
(x, y)→(-y, -x)
(x, y)→(-x, -y)
(x, y)→(y, -x)
(x, y)→(-y, x)
A transformation that does not change the size or shape of a pre-image (pre-image and image are congruent) is called
Rigid Motion Transformation
Dilation
Non-Isometric
Non- Rigid Motion Transformation
Similar Figure Transformation
Which is NOT an Isometry?
Relection
Dilation
Rotation
Translation
Not Enough Information
Identify the smallest angle of rotation that maps the image to itself.
90°
180°
45°
60°
30°
A rigid motion creates figures that are ____________.
congruent
different sizes
similar
larger
dilated figures
A rigid motion ...
preserves size and location
preserves shape and location
preserves size and shape
makes the figure larger
preserves shape and the size is different by a scale factor
What are the series of rigid motions that would map ∆ABC onto ∆A''B''C''?
a reflection followed by a rotation
a reflection followed by a translation
a translation followed by a rotation
a translation followed by a reflection
a rotation followed by a translation
Which of the following transformation will map the regular pentagon onto itself, choose ALL that apply?
x axis reflection
y axis reflection
90 degree rotation
180 degree rotation
72 degree rotation around the orgin
Which of the following transformation will map the trapezoid onto itself, choose ALL that apply?
x axis reflection
reflection across green line
rotation 90 degrees about (2,-1)
reflection across the blue line
rotation 180 degrees about (2,-1)
Which of the following transformation will map the regular pentagon onto itself?
reflection across blue line
reflection across green line
108 degree rotation about the origin
216 degree rotation about the origin
None of the transformation map onto the original penatgon
Which transformation will map the rectangle onto itself?
90 degree rotation about (-2,1)
540 degree rotation about (-2,1)
reflection across the y-axis
reflection across the blue line
reflection across the x-axis
Which of the following transformations will NOT map the regular hexagon onto itself?
270 degree rotation about the origin
x axis reflection
y axis reflection
180 degree rotation about the origin
120 degree rotation about the origin
Which of the Transformations will map the trapezoid onto itself choose ALL that apply?
180 degree rotation about the origin
180 degree rotation about (-4.5, 3.5)
reflection across the blue line
reflection across the green line
90 degree rotation about (-4.5, 3.5)
Which transformation will map the parallelogram onto itself?
reflection x axis
reflection y axis
refection across the green line
reflection over the line y=x
none of these above
Select each answer choice that will map the regular polygon onto itself?
36 degree rotation
90 degree rotation
180 degree rotation
252 degree rotation
270 degree rotation
Select each answer choice that will map the regular polygon onto itself
x axis reflection
y axis reflection
reflection across the green line
none of thee above
which transformation will map the regular octagon onto itself?
30 degree rotation about the center
45 degree rotation about the center
120 degree rotation about the center
225 degree rotation about the center
270 degree rotation about the center
When performing 2 reflections over parallel lines (as shown in the diagram) what is the resultant transformation?
1 Reflection
1 Rotation
1 Translation
1 Dilation
Not enough information
When performing 2 reflections over non-parallel lines (as shown in the diagram) what is the resultant transformation?
1 Reflection
1 Rotation
1 Translation
1 Dilation
Not enough information
Which transformation will map an image onto itself?
A translation 3 units right and 3 units up
A rotation 360o clockwise
A reflection over the y-axis followed by a translation 3 units down
A dilation followed by a 90o clockwise rotation
Not enough information, a figure has to be given!
Which of the following is the construction of an equilateral triangle given side AB?
Not enough information without labeled side lengths
A line perpendicular to one of two parallel lines is perpendicular to the other.
Two lines are perpendicular if they intersect to form congruent adjacent angles.
When two lines are intersected by a traversal and alternate interior angles are congruent, the lines are parallel.
When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel.
When two lines are intersected by a traversal and same side exterior angles are congruent, the lines are parallel.
The following shows the steps of which construction?
inscribed triangle
inscribed hexagon
circumscribed square
inscribed square
circumscribed rhombus
