Tenth Grade (Grade 10) Symmetry and Transformations Questions for Tests and Worksheets

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Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.2

Señor Domínguez made the following conjecture: "Any transformation of triangle LMN on a coordinate grid results in a congruent image."

Which transformation represents a counterexample to this statement?

Triangle LMN is relfected over the line y = -5.
Triangle LMN is translated 4 units left and 2 units down.
Triangle LMN is rotated 90° counterclockwise about the origin.
Triangle LMN is dilated with a scale factor of 2 about the origin.

Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

The coordinates of the vertices of

$Delta CDE$ are C(-4,-4), D(-1,-1), and E(0,5). The coordinates of the vertices of

$Delta JKL$ are J(-8,8), K(-2,2), and L(10,0). Which of the following sequence of transformations, applied to

$Delta CDE$ , shows that

$Delta CDE \ ~ \ Delta JKL ?$

A rotation of 90° counterclockwise about the origin, and then a dilation of factor -2 centered at the origin.
A reflection over the line $y=2$ , and then a dilation of factor 2 centered at the origin.
A translation of 2 units left and 4 units up, and then a dilation of factor 2 centered at the origin.
A reflection over the line $y=x$ , and then a dilation of factor $-2$ centered at the origin.

Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.3

Which of the following shapes has only one transformation (rotation less than 360° or reflection) that will map it onto itself?

Equilateral triangle
Isosceles trapezoid
Regular dodecagon
Rectangle

Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.3

Which of the following are valid transformations that will always map a rectangle onto itself? There may be more than one correct answer.

Rotate about its center 180°.
Rotate about its center 90°.
Reflect over either diagonal.
Reflect over either line segment joining midpoints of opposite sides.

Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

This question is a part of a group with common instructions. View group »

What are the coordinates of the transformed points, P', Q', R', if they are rotated 90° clockwise about the origin and then translated 4 units to the left?

(-3, -2), (0, -1), (1, -4)
(-5, 2), (-8, 1), (-9, 4)
(1, 2), (4, 3), (5, 0)
(-6, -1), (-5, -4), (-8, -5)

Grade 10 Symmetry and Transformations

What kind of symmetry does this shape have?

Rotational Symmetry
Line Symmetry
No Symmetry
Both a & b

Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.4

Triangle ABC is translated 7 units right and 3 units up. The translated image is A'B'C' (not shown). Ellen believes that quadrilateral B'BCC' is a parallelogram and gives the following reasoning why. She knows that because rigid transformations do not change the size of a line segment, that

$bar{B C} ~= bar{C' B'}$ . Also,

$bar(B B') ~= bar{C C'}$ since line segments formed by corresponding points of translated images are congruent. James disagrees with her and says that she has not shown quadrilateral B'BCC' is a parallelogram. Who is correct and why?

Ellen is correct. Her statements are correct and sufficient to conclude that B'BCC' is a parallelogram.
James is correct. Although Ellen's statements are correct, they are not sufficient to conclude that B'BCC' is a parallelogram.
James is correct. Ellen's reasoning as to why $bar(B B') ~= bar{C C'}$ is not incorrect.
James is correct. There are other ways to prove B'BCC' is a parallelogram.

Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

This question is a part of a group with common instructions. View group »

Aside from calculating the length of each line segment, what reasoning can be used to conclude that

$bar{PQ}~= bar{P'Q'}$ and

$bar{QR} ~= bar{Q'R'} ?$

They have similar names.
The points which define them were transformed by the same rigid transformations.
Reflections were not involved in the transformations.
They are specified by Cartesian coordinates.

Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

This question is a part of a group with common instructions. View group »

Because the three sides of ABC can be mapped by the same sequence of rigid transformations to the three sides of triangle LMN, what does this imply and why?

$Delta ABC ~= Delta LMN$ , since no rotations were used.
$Delta ABC ~= Delta LMN$ , since rigid transformations preserve size and shape.
The triangles are not necessarily congruent, since we know nothing about the angles.
The triangles are not necessarily congruent, since each side was considered separately.

Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

This question is a part of a group with common instructions. View group »

Would the sequence of transformations that mapped

$bar{AB}$ onto

$bar{LM}$ be the same for mapping

$bar{AC}$ onto

$bar{LN}$ and

$bar{BC}$ onto

$bar{MN} ?$

No.
Only for mapping $bar{AC}$ onto $bar{LN}$ .
Only for mapping $bar{BC}$ onto $bar{NM}$ .
Yes.

Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.1

Point A'(12,4) is the image of point A(3,1) under a dilation with respect to the origin. What is the constant of dilation?

9
$1/4$
3
4

Grade 10 Symmetry and Transformations

When a figure is rotated about a point, the direction of rotation is always counter-clockwise.

True
False

Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.4

Quadrilateral ABCD is reflected over line

$l$ . Its image is A'B'C'D'. What can be said about the relationship between line segment

$bar(A A')$ and line

$l ?$ Choose all correct answers.

$l$ and $bar(A A')$ are perpendicular.
$l$ and $bar(A A')$ are parallel.
$l$ and $bar(A A')$ do not intersect.
$l$ bisects $bar(A A')$ .

Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.4

The coordinates of triangle ABC's vertices are located at

$(2,3), (4,5),$ and

$(5,1)$ , respectively. Triangle ABC is translated 5 units right and 3 units down, which we can call triangle A'B'C'. Of the three line segments formed by this translation,

$bar{A A'}, bar{B B'},$ and

$bar{C C'}$ , which is the shortest?

$bar{A A'}$
$bar{BB'}$
$bar{C C'}$
They are all the same length.

Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.2

A Nonrigid Transformation is a transformation in which the image is congruent to the preimage.

True
False

Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.4

Given quadrilateral ABCD, you rotate it

$x$ degrees counterclockwise about the point

$O$ , resulting in the transformed image, A'B'C'D'. Which of the following are true? Choose all correct answers.

$bar{A O} _|_ bar{A'O}$
$m ang AOA' = 180° - x°$
$bar(A O) ~= bar(A' O)$
$m ang AOA' = x°$

Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.4

Triangle ABC is reflected over a line to produce its image, triangle A'B'C'. The vertices of triangle ABC are

$(1,1), (1,4), (4,1)$ . The vertices of its image are

$(6.6, 3.8), (4.2, 5.6), (4.8, 1.4)$ . What is the line over which triangle ABC was reflected?

Cannot be determined.
$y=1/2 x +1/2$
$y=-2x+7$
$y=-2x+10$

Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.4

Square ABCD is translated horizontally and vertically. Its translated image is A'B'C'D'. What is true about the line segments

$bar{A A'}$ and

$bar{B B'} ?$ There may be more than one correct answer.

They are parallel.
They are perpendicular.
They are equal in length.
They bisect each other.

Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

$Delta EFG$ has vertices located at E(3,7), F(-1,4), and G(2,1).

$Delta TUV$ has vertices located at T(-9,15), U(-1,9), and V(-7,3). Which of the following sequences of transformations, applied to

$Delta EFG$ , shows that

$Delta EFG \ ~ \ Delta TUV ?$

A translation of 1 unit right and 1 unit up, a rotation of 90° counterclockwise about the origin, and then a dilation of factor 2 centered at the origin.
A translation of 6 units right and 4 units down, a rotation of 90° about the origin, and then a dilation of factor 2 centered at (3,3).
A translation of 1 unit right and 1 unit up, a reflection over the y-axis, and then a dilation of factor 2 centered at (1,1).
A translation of 3 units left and 4 units up, and then a dilation of factor $3/2$ centered at the origin.

Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

The coordinates of the vertices of

$Delta FGH$ are

$F(0,1)$ ,

$G(3,-1)$ , and

$H(5,3)$ . The coordinates of the vertices of

$Delta SRT$ are

$S(0,-1)$ ,

$R(3/2,0)$ , and

$T(5/2, -2)$ . Which of the following sequences of transformations, applied to

$Delta FGH$ , shows that

$Delta FGH \ ~ \ Delta SRT ?$

A translation 2 units down, and then a dilation by a factor of $1/2$ centered at the origin.
A rotation of 180° about the origin, and then a dilation by a factor of $1/2$ centered at the origin.
A translation of a $1/2$ unit up, and then a dilation by a factor of $1/2$ centered at the origin.
A translation of 1 unit up, a reflection over the x-axis, and then a dilation by a factor of $1/2$ centered at the origin.

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Tenth Grade (Grade 10) Symmetry and Transformations Questions