Transformations in the Plane

Last updated over 5 years ago

15 questions

Note from the author:

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Library

Transformations in the Plane

Last updated over 5 years ago

15 questions

Note from the author:

Used for geometry. Students answer review questions about different transformations. 

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A regular nonagon has 9 sides. What is the smallest angle of rotation about its center that carries a nonagon onto itself?

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Draggable item		Corresponding Item

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Used for geometry. Students answer review questions about different transformations. 

Triangles ABC and A'B'C' are shown below. Which of the following transformations takes triangle ABC onto triangle A'B'C'?

(x, y) → (− y, − x)

(x, y) → (x, y)

(x, y) → (y, x)

(x, y) → (− x, − y)

A triangle with coordinates A (1, 1) , B (4, 2) , C (3, 5) is translated three units down and five units to the left.
What are the coordinates of the new triangle?

A′ (−4, − 2), B′ (−1, − 3), C′ (−2, − 6)

A′ (−2, − 4), B′ (1, − 3),  C′ (0, 0)

A′ (−4, − 2), B′ (−7, − 3), C′ (−6, 0)

A′ (−4, − 2), B′ (−1, − 1), C′ (−2, 2)

Triangle ABC is reflected over the line y = 1 to produce triangle A'B'C'. What will be the coordinates of A'?

(4, 1)

(2, 1)

(2, 0)

(4, 3)

Triangle ABC is translated to triangle A'B'C' by the following motion rule.
(x, y) → (x + 2, y − 5)

What will be the coordinates of C'?

(0, 2)

(−1, − 3)

(−3, − 2)

(− 5, −3)

The vertices of ∆ ABC are A (− 4, 2) , B (6, 6) , C (2, 7). A translation maps point A to the point A′ (4, 0) . If B and C are mapped by the same translation, what are the coordinates of B' and C'?

B′ (14, 4), C′ (10, 5)

B′ (− 6, 4), C′ (− 2, 5)

B′ (10, 8), C′ (6, 9)

B′ (8, 5), C′ (4, 6)

In this diagram where is the line of reflection?

x = 1

x = 0

y = 2

y = 3.5

A regular nonagon has 9 sides. What is the smallest angle of rotation about its center that carries a nonagon onto itself?

Patrick rotated an octagon about its center. What degree measure could he have rotated the octagon so that it mapped onto itself?

120°

300°

315°

60°

Look at AB on the coordinate plane. State the coordinates of B' after a 90 degree counterclockwise rotation about the origin.

(-3, -4)

(3, 4)

(-4, -3)

(4, 3)

After examining the following graph, Kate claims that WXYZ is translated according to the rule:
(x, y) → (x + 11, y − 2).

Is she correct?

Yes, Kate is correct.

No, WXYZ is translated by the rule: (x, y) → (x − 11, y + 2).

No, WXYZ is translated by the rule: (x, y) → (x + 2, y − 11).

No, WXYZ is translated by the rule: (x, y) → (x − 2, y + 11).

A transformation that preserves length and angle measure is:

a rigid motion

a non-rigid motion

a corresponding figure

a pre-image

A dilation is a rigid motion.

True

False

The ______________ is the resulting figure after a transformation.

coordinate

image

motion

pre-image

Match the transformation with its picture. (Click the word, then click the picture to match them up.)

Draggable item		Corresponding Item
rotation
dilation
reflection
translation

Which does NOT describe a way to map this square back onto itself?

A reflection in the x-axis

A 90° counterclockwise rotation about (-2, 0)

A 270° counterclockwise rotation about the origin

A reflection in x = -2

Triangles ABC and A'B'C' are shown below. Which of the following transformations takes triangle ABC onto triangle A'B'C'?

(x, y) → (− y, − x)

(x, y) → (x, y)

(x, y) → (y, x)

(x, y) → (− x, − y)

A triangle with coordinates A (1, 1) , B (4, 2) , C (3, 5) is translated three units down and five units to the left.
What are the coordinates of the new triangle?

A′ (−4, − 2), B′ (−1, − 3), C′ (−2, − 6)

A′ (−2, − 4), B′ (1, − 3),  C′ (0, 0)

A′ (−4, − 2), B′ (−7, − 3), C′ (−6, 0)

A′ (−4, − 2), B′ (−1, − 1), C′ (−2, 2)

Triangle ABC is reflected over the line y = 1 to produce triangle A'B'C'. What will be the coordinates of A'?

(4, 1)

(2, 1)

(2, 0)

(4, 3)

Triangle ABC is translated to triangle A'B'C' by the following motion rule.
(x, y) → (x + 2, y − 5)


What will be the coordinates of C'?

(0, 2)

(−1, − 3)

(−3, − 2)

(− 5, −3)

The vertices of ∆ ABC are A (− 4, 2) , B (6, 6) , C (2, 7). A translation maps point A to the point A′ (4, 0) . If B and C are mapped by the same translation, what are the coordinates of B' and C'?

B′ (14, 4), C′ (10, 5)

B′ (− 6, 4), C′ (− 2, 5)

B′ (10, 8), C′ (6, 9)

B′ (8, 5), C′ (4, 6)

In this diagram where is the line of reflection?

x = 1

x = 0

y = 2

y = 3.5

Patrick rotated an octagon about its center. What degree measure could he have rotated the octagon so that it mapped onto itself?

120°

300°

315°

60°

Look at AB on the coordinate plane. State the coordinates of B' after a 90 degree counterclockwise rotation about the origin.

(-3, -4)

(3, 4)

(-4, -3)

(4, 3)

After examining the following graph, Kate claims that WXYZ is translated according to the rule:
(x, y) → (x + 11, y − 2). 

Is she correct?

Yes, Kate is correct.

No, WXYZ is translated by the rule: (x, y) → (x − 11, y + 2).

No, WXYZ is translated by the rule: (x, y) → (x + 2, y − 11).

No, WXYZ is translated by the rule: (x, y) → (x − 2, y + 11).

A transformation that preserves length and angle measure is:

a rigid motion

a non-rigid motion

a corresponding figure

a pre-image

A dilation is a rigid motion.

True

False

The ______________ is the resulting figure after a transformation.

coordinate

image

motion

pre-image

Match the transformation with its picture. (Click the word, then click the picture to match them up.)

rotation

dilation

reflection

translation

Which does NOT describe a way to map this square back onto itself?

A reflection in the x-axis

A 90° counterclockwise rotation about (-2, 0)

A 270° counterclockwise rotation about the origin

A reflection in x = -2

Transformations in the Plane

Transformations in the Plane

A regular nonagon has 9 sides. What is the smallest angle of rotation about its center that carries a nonagon onto itself?

Triangles ABC and A'B'C' are shown below. Which of the following transformations takes triangle ABC onto triangle A'B'C'?

A triangle with coordinates A (1, 1) , B (4, 2) , C (3, 5) is translated three units down and five units to the left.What are the coordinates of the new triangle?

Triangle ABC is reflected over the line y = 1 to produce triangle A'B'C'. What will be the coordinates of A'?

Triangle ABC is translated to triangle A'B'C' by the following motion rule.(x, y) → (x + 2, y − 5)What will be the coordinates of C'?

The vertices of ∆ ABC are A (− 4, 2) , B (6, 6) , C (2, 7). A translation maps point A to the point A′ (4, 0) . If B and C are mapped by the same translation, what are the coordinates of B' and C'?

In this diagram where is the line of reflection?

A regular nonagon has 9 sides. What is the smallest angle of rotation about its center that carries a nonagon onto itself?

Patrick rotated an octagon about its center. What degree measure could he have rotated the octagon so that it mapped onto itself?

Look at AB on the coordinate plane. State the coordinates of B' after a 90 degree counterclockwise rotation about the origin.

After examining the following graph, Kate claims that WXYZ is translated according to the rule:(x, y) → (x + 11, y − 2). Is she correct?

A transformation that preserves length and angle measure is:

A dilation is a rigid motion.

The ______________ is the resulting figure after a transformation.

Match the transformation with its picture. (Click the word, then click the picture to match them up.)

Which does NOT describe a way to map this square back onto itself?

A triangle with coordinates A (1, 1) , B (4, 2) , C (3, 5) is translated three units down and five units to the left.
What are the coordinates of the new triangle?

Triangle ABC is translated to triangle A'B'C' by the following motion rule.
(x, y) → (x + 2, y − 5)

What will be the coordinates of C'?

After examining the following graph, Kate claims that WXYZ is translated according to the rule:
(x, y) → (x + 11, y − 2).

Is she correct?