Question 1

In the diagram, congruent figures 1, 2, and 3 are drawn.  Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3?

Accepted Answer

a translation followed by a rotation

Answer

a rotation followed by a translation

Answer

a translation followed by a reflection

Answer

a reflection followed by a translation

Question 2

Which regular polygon has a minimum rotation of 45° to carry the polygon onto itself?

Accepted Answer

octagon

Answer

pentagon

Answer

decagon

Answer

hexagon

Question 3

A reflection over which line does NOT carry the square onto itself?

Accepted Answer

x = 5

Answer

y = 2

Answer

y + x = 4

Answer

y = x

Question 4

Is ∆ABC $\cong$∆XYZ?

Accepted Answer

Yes - a 180˚ rotation centered at the origin maps ∆ABC onto ∆XYZ

Answer

Yes - a reflection over the line y = -x  maps ∆ABC onto ∆XYZ

Answer

Yes - a reflection over the x-axis maps ∆ABC onto ∆XYZ

Answer

Yes - a reflection over the y-axis maps ∆ABC onto ∆XYZ

Question 5

Which sequence of transformations maps triangle ABC onto triangle DEF?

Accepted Answer

a reflection over the x-axis followed by a reflection over the y-axis

Answer

a translation 8 units to the right and 1 unit up followed by a 90˚ counterclockwise rotation centered at the origin

Answer

a 180˚rotation centered at the origin followed by a reflection over the line y = x

Answer

a 90˚ clockwise rotation centered at the origin followed by a reflection over the y-axis

Question 6

Which statement explains why ∆ABC $\cong$∆A'B'C'?

Accepted Answer

A translation three units down followed by a reflection over the y-axis

Answer

A translation six units left and three units down.

Answer

A translation three units down followed by a reflection over the x-axis

Answer

A translation three units down and two units left

Question 7

Which sequence of transformations maps rectangle ABCD onto rectangle A'B'C'D' and then maps rectangle A'B'C'D'  onto rectangle A"B"C"D" ?

Accepted Answer

a reflection followed by a rotation

Answer

a reflection followed by a translation

Answer

a translation followed by a rotation

Answer

a translation followed by a reflection

Question 8

In the diagram, which single transformation was used to map triangle A onto triangle B?

Accepted Answer

rotation

Answer

translation

Answer

line reflection

Answer

dilation

Question 9

Which transformation of OA will result in an image parallel to OA?

Accepted Answer

a translation three units down

Answer

a reflection over the y-axis

Answer

a rotation of 90˚ clockwise centered at the origin

Answer

a reflection over the x-axis

Question 10

Which sequence of rigid motions maps ∆ABC onto ∆DEF?

Accepted Answer

reflection over the x-axis followed by a translation right six units

Answer

translation right six units and down six units

Answer

reflection over the y-axis followed by a translation right six units

Answer

reflection over the x-axis followed by a translation right three units

Question 11

Which transformation can prove rectangle ABCD congruent to rectangle KLMN?

Accepted Answer

reflection over the x-axis

Answer

rotation

Answer

reflection over the y-axis

Answer

reflection

Question 12

Which transformation would not always produce an image that would be congruent to the original figure?

Accepted Answer

dilation

Answer

reflection

Answer

rotation

Answer

translation

Question 13

A regular hexagon is rotated in a counterclockwise direction about its center. Determine and state the minimum number of degrees in the rotation such that the hexagon will carry onto itself.

Accepted Answer

60

Question 14

Under which transformation would ∆A'B'C', the image of ∆ABC, NOT be congruent to ∆ABC?

Accepted Answer

dilation with a scale factor of 2 centered at the origin

Answer

translation of 3 units right and 2 units down

Answer

reflection over the y-axis

Answer

rotation of 90˚ clockwise centered at the origin

Question 15

Which sequence of transformations could map pentagon ABCDE onto pentagon A'B'C'D'E'?

Accepted Answer

line reflection followed by a translation

Answer

translation followed by a rotation

Answer

dilation followed by a rotation

Answer

line reflection followed by a line reflection

Question 16

Which rotation about its center will carry a regular decagon onto itself?

Accepted Answer

252˚

Answer

54˚

Answer

162˚

Answer

198˚

Question 17

Which transformation explains why ∆ABC $\cong$∆A"B"C"?

Accepted Answer

a reflection over the y-axis followed by a translation up 2

Answer

a translation right 4 and up 2

Answer

a reflection over the x-axis followed by a translation up 2

Answer

a reflection over the y-axis

Question 18

In the diagram, ∆ABC $\cong$∆DEF.  Which sequence of transformations maps ∆ABC onto ∆DEF?

Accepted Answer

a reflection over the y-axis followed by a translation

Answer

a reflection over the x-axis followed by a translation

Answer

a counterclockwise rotation of 90° centered at the origin followed by a translation

Answer

a rotation of 180° centered at the origin followed by a translation

Question 19

Which figure always has exactly four lines of reflection that carry the figure onto itself?

Accepted Answer

square

Answer

rectangle

Answer

regular octagon

Answer

equilateral triangle

Question 20

The image of ∆DEF is ∆D'E'F'. Under which transformation will the triangles NOT be congruent?

Accepted Answer

a dilation with a scale factor of 2 centered at the origin

Answer

a reflection through the origin

Answer

a dilation with a scale factor of 1 centered at (2,3)

Answer

a reflection over the line y = x

Question 21

Which transformation would NOT carry the rectangle onto itself?

Accepted Answer

a rotation of 180° centered at the origin

Answer

a rotation of 180° centered at the point (4,0)

Answer

a reflection over the x-axis

Answer

a reflection over the line x = 4

Question 22

A regular decagon is rotated n degrees about its center, carrying the decagon onto itself. The value of n could be

Accepted Answer

252˚

Answer

10˚

Answer

225˚

Answer

150˚

Question 23

Which transformation does NOT map MATH onto M"A"T"H"?

Accepted Answer

A 180˚ rotation centered at the origin

Answer

A translation up one and left one followed by a 180˚ rotation centered at (-1,1)

Answer

A 180˚ rotation centered at (-0.5, 0.5)

Answer

A reflection over the line x = -0.5 followed by a reflection over the line y = 0.5

Question 24

In the diagram below, a sequence of rigid motions maps ABCD onto JKLM.  If m∠A = 82°, m∠B = 104°, and m∠L = 121°, the measure of ∠M is

Accepted Answer

53˚

Answer

121˚

Answer

104˚

Answer

82˚

Question 25

The graph below shows two congruent triangles, ABC and A'B'C'.  Which rigid motion would map ∆ABC onto ∆A'B'C'?

Accepted Answer

a reflection over the line y = x

Answer

a translation of three units to the left and three units up

Answer

a rotation of 180 degrees centered at the origin

Answer

a rotation of 90 degrees counterclockwise centered at the origin

Question 26

The vertices of ∆PQR have coordinates P(2,3), Q(3,8), and R(7,3). Under which transformation of ∆PQR are distance and angle measure preserved?

Accepted Answer

(x, y)→(x + 2, y + 3)

Answer

(x, y)→(2x, 3y)

Answer

(x, y)→(2x, y + 3)

Answer

(x, y)→(x + 2, 3y)

Question 27

Which transformation would NOT carry a square onto itself?

Accepted Answer

a 180° rotation about one of its vertices

Answer

a reflection over the perpendicular bisector of one side

Answer

a 90° rotation clockwise about its center

Answer

a reflection over one of its diagonals

Question 28

After a counterclockwise rotation about point X, scalene triangle ABC maps onto  ∆RST, as shown in the diagram.  Which statement must be true?

Accepted Answer

∠A $\cong$∠R

Answer

CA $\cong$TS

Answer

∠A $\cong$∠S

Answer

CB $\cong$TR

Question 29

In the diagram below, line m is parallel to line n. Figure 2 is the image of Figure 1 after a reflection over line m. Figure 3 is the image of Figure 2 after a reflection over line n.  Which single transformation would carry Figure 1 onto Figure 3?

Accepted Answer

a translation

Answer

a dilation

Answer

a rotation

Answer

a reflection

Question 30

Which angle of rotation will carry a regular pentagon onto itself?

Accepted Answer

216˚

Answer

54˚

Answer

180˚

Answer

108˚

Question 31

Which sequence of transformations will map quadrilateral BIKE onto quadrilateral GOLF.

Accepted Answer

a translation up 5 units followed by a reflection over the y-axis

Answer

a translation up 5 units and right 8 units

Answer

a reflection over the y-axis followed by a translation up 4 units

Answer

a reflection over the x-axis followed by a translation up 5 units

Question 32

In regular hexagon ABCDEF, AD, BE , and CF all intersect at G.  When  ∆ABG is reflected over BG and then rotated 180° about point G, ∆ABG is mapped onto

Accepted Answer

∆FEG

Answer

∆CBG

Answer

∆AFG

Answer

∆DEG

Question 33

Which transformation will NOT carry the rectangle onto itself?

Accepted Answer

a rotation of 180° about the point (6,6)

Answer

a reflection over the line y = -x + 10

Answer

a rotation of 180° about the point (5,5)

Answer

a reflection over the line y =  x

Question 34

Which sequence of transformations does NOT map trapezoid ABCD onto trapezoid A"B"C"D"?

Accepted Answer

A reflection over the y-axis followed by a reflection over the x = -1

Answer

A 180˚ rotation centered at (0, -1)

Answer

A 180˚ rotation centered at the origin followed by a translation down 2 units

Answer

A reflection over the y-axis followed by a reflection over y = -1

Question 35

In the diagram below, ∆ABC with sides of 13, 15, and 16, is mapped onto ∆DEF after a clockwise rotation of 90° centered at point P.  What is the value of x?

Accepted Answer

8.5

Answer

7

Answer

8

Answer

7.5

Question 36

The figure below shows a rhombus with non-congruent diagonals.  Which transformation would NOT carry this rhombus onto itself?

Accepted Answer

a clockwise rotation of 90° centered at the intersection of the diagonals

Answer

a reflection over the shorter diagonal

Answer

a counter clockwise rotation of 180° about the intersection of the diagonals

Answer

a reflection over the longer diagonal

Question 37

Which sequence of transformations would NOT map ∆ABC onto ∆QRS?

Accepted Answer

A reflection over the x-axis followed by a 90˚ clockwise rotation centered at the origin.

Answer

A reflection over the line y = x + 4

Answer

A translation three units left and three units up followed by a rotation 90˚ counterclockwise centered at (-5, 2) followed by a reflection over x = -5

Answer

A reflection over y = x followed by a translation left four units and up 4 units

Question 38

Triangles JOE and SAM are drawn such that ∠E $\cong$∠M and 
EJ $\cong$MS. Which mapping would NOT always lead to
∆JOE $\cong$∆SAM?

Accepted Answer

JO maps onto SA

Answer

∠J maps onto ∠S

Answer

EO maps onto MA

Answer

∠O maps onto ∠A

Question 39

On the set of axes below, triangle ABC is graphed. Triangles A'B'C'  and A"B"C" , the images of triangle ABC, are graphed after a sequence of rigid motions.  Identify which sequence of rigid motions maps ∆ABC onto ∆A'B'C', and then maps ∆A'B'C' onto ∆A"B"C" .

Accepted Answer

a reflection followed by a rotation

Answer

a translation followed by a reflection

Answer

a reflection followed by a translation

Answer

a rotation followed by another rotation

Question 40

Which transformation carries the parallelogram onto itself?

Accepted Answer

a rotation of 180° counterclockwise about the origin

Answer

a reflection over y = -x

Answer

a rotation of 90° counterclockwise about the origin

Answer

a reflection over y = x

Question 41

Which sequence of rigid motions maps ∆ABC onto ∆STU?

Accepted Answer

A 90˚ counter clockwise rotation centered at the origin

Answer

A translation right 3 units and down 7 units

Answer

A 90˚ clockwise rotation centered at the origin

Answer

A translation right 2 units and down 6 units

Question 42

Which transformation would carry the rhombus onto itself?

Accepted Answer

reflection over the line x = 0

Answer

reflection over the line y = $\frac{1}{2}$x + 1

Answer

180° rotation counterclockwise centered at the origin

Answer

reflection over the line y = 0

Question 43

A regular hexagon is rotated about its center. Which degree measure will carry the regular hexagon onto itself?

Accepted Answer

120˚

Answer

90˚

Answer

45˚

Answer

135˚

Question 44

If ∆A'B'C' is the image of ∆ABC, under which transformation will the triangles NOT be congruent?

Accepted Answer

dilation centered at the origin with scale factor 2

Answer

rotation of 270° counterclockwise about the origin

Answer

translation to the left 5 and down 4

Answer

reflection over the x-axis

Question 45

Which transformation would result in the perimeter of a triangle being different from the perimeter of its image?

Accepted Answer

(x, y) → (4x, 4y)

Answer

(x, y) → (y, x)

Answer

(x, y) → (x + 2, y - 5)

Answer

(x, y) → (x, -y)

Question 46

Which sequence of rigid motions will prove ∆ABC $\cong$∆RST?

Accepted Answer

a rotation of 180° centered at (1,0)

Answer

a line reflection over y = x

Answer

a line reflection over the x-axis followed by a line reflection over y = 1

Answer

a line reflection over the x-axis followed by a translation of 6 units right

Question 47

Rhombus ABCD can be mapped onto rhombus KLMN by a rotation about point P.  What is the measure of ∠KNM if the measure of ∠CAD = 35˚?

Accepted Answer

110˚

Answer

70˚

Answer

55˚

Answer

35˚

Question 48

Pentagon ABCDE is congruent to A"B"C"D"E".  Which describes a sequence of rigid motions that maps ABCDE onto A"B"C"D"E"?

Accepted Answer

a rotation of 90° counterclockwise about the origin followed by a translation down 7 units

Answer

a reflection over the x-axis followed by a rotation of 90° counterclockwise about the origin

Answer

a reflection over the y-axis followed by a reflection over the x-axis

Answer

a rotation of 90° counterclockwise about the origin followed by a reflection over the x-axis

Question 49

A regular octagon is rotated about its center.  What is the minimum number of degrees needed to carry the octagon onto itself?

Accepted Answer

45

Question 50

A regular polygon, when rotated 24˚ about its center, carries onto itself for the first time.  How many sides does the polygon have?

Accepted Answer

15

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