Section 2 Further Transformations

Question 1

What is a transformation in mathematics?

Answer 1

A transformation is a function that maps a set of points to another set of points in a specific way.

Question 2

True or False: A translation moves a figure without changing its shape or size.

Answer 2

True

Question 3

What type of transformation flips a figure over a line?

Answer 3

Reflection

Question 4

Fill in the blank: A __________ transformation stretches or shrinks a figure.

Answer 4

dilation

Question 5

What is the center of dilation?

Answer 5

The point around which a figure is enlarged or reduced.

Question 6

True or False: Rotations can only occur in a clockwise direction.

Answer 6

False

Question 7

What is the angle of rotation in a transformation?

Answer 7

The degree measure that indicates how far a figure is rotated.

Question 8

Multiple Choice: Which transformation does NOT change the size of a figure? A) Dilation B) Translation C) Reflection

Answer 8

B) Translation

Question 9

What is the line of reflection?

Answer 9

The line over which a figure is reflected to create a mirror image.

Question 10

True or False: A rotation can be defined by its center and angle.

Answer 10

True

Question 11

What does it mean to perform a composite transformation?

Answer 11

To apply two or more transformations in sequence.

Question 12

Fill in the blank: A __________ is a transformation that changes the position of a figure without altering its shape or size.

Answer 12

translation

Question 13

What is the result of a reflection over the x-axis?

Answer 13

The y-coordinates of the points are multiplied by -1.

Question 14

Multiple Choice: Which of the following transformations is NOT rigid? A) Translation B) Dilation C) Reflection

Answer 14

B) Dilation

Question 15

What is a rigid transformation?

Answer 15

A transformation that preserves distance and angle measures.

Question 16

True or False: The transformation of a figure can change its orientation.

Answer 16

True

Question 17

What is the formula for a dilation centered at the origin?

Answer 17

If (x, y) is a point, the dilated point is (kx, ky) where k is the scale factor.

Question 18

Fill in the blank: A __________ transformation rotates a figure around a fixed point.

Answer 18

rotation

Question 19

What does the scale factor indicate in a dilation?

Answer 19

How much the figure is enlarged or reduced.

Question 20

True or False: A reflection can occur over any line, not just the axes.

Answer 20

True

Question 21

What is the effect of a counterclockwise rotation of 90 degrees?

Answer 21

The coordinates (x, y) become (-y, x).

Question 22

Multiple Choice: After a dilation with a scale factor of 1/2, what happens to the size of the figure? A) It doubles B) It halves C) It remains the same

Answer 22

B) It halves

Question 23

What is the composition of transformations?

Answer 23

The result of applying multiple transformations one after another.

Question 24

Fill in the blank: The __________ of a transformation describes how it affects the position and shape of figures.

Answer 24

nature

Question 25

True or False: A translation can be represented by a vector.

Answer 25

True

Question 26

What is the geometric interpretation of a reflection over the line y = x?

Answer 26

The coordinates (x, y) are transformed to (y, x).

Question 27

What does it mean for a transformation to be non-rigid?

Answer 27

It changes the shape or size of the figure.

Question 28

Multiple Choice: Which transformation is represented by the equation (x, y) -> (x + 3, y - 2)? A) Reflection B) Translation C) Dilation

Answer 28

B) Translation

Question 29

What is the outcome of a reflection over the y-axis?

Answer 29

The x-coordinates of the points are multiplied by -1.

Question 30

Fill in the blank: A __________ is a specific type of transformation that results in a change of position.

Answer 30

translation

Question 31

True or False: The order of transformations matters in composite transformations.

Answer 31

True

Question 32

What is the fixed point in a rotation called?

Answer 32

The center of rotation.

Question 33

Multiple Choice: Which transformation preserves the shape and size of a figure? A) Dilation B) Translation C) Reflection

Answer 33

B) Translation

Question 34

What happens to a figure during a 180-degree rotation?

Answer 34

The coordinates (x, y) become (-x, -y).

Question 35

Fill in the blank: The __________ of transformation refers to how the figure is altered in position or size.

Answer 35

effect

Question 36

What is a transformation matrix?

Answer 36

A matrix used to perform transformations on geometric figures.

Question 37

True or False: A transformation can be represented graphically.

Answer 37

True

Question 38

What is the purpose of using transformations in geometry?

Answer 38

To analyze and manipulate shapes and their properties.