Master Geometry Transformations: Enhance Your Math Education Skills

Question 1

What is the center of rotation when a figure is rotated 180 degrees?

Accepted Answer

The midpoint of the figure

Answer

Any point on the figure

Answer

The origin

Answer

Outside the figure

Question 2

If a figure is reflected across the y-axis, what is the effect on its x-coordinates?

Accepted Answer

They are multiplied by -1

Answer

They are multiplied by 1

Answer

They are not affected

Answer

They are divided by 2

Question 3

Which of the following transformations is a combination of a translation and a rotation?

Accepted Answer

Glide reflection

Answer

Dilation

Answer

Homothety

Answer

Isometry

Question 4

If a point (x, y) is reflected across the line y = x, what are the coordinates of the reflected point?

Accepted Answer

(y, x)

Answer

(x, -y)

Answer

(-x, y)

Answer

(-y, x)

Question 5

What is the image of point (2, 3) under the translation (x, y) -> (x + 1, y - 2)?

Accepted Answer

(3, 5)

Answer

(1, 1)

Answer

(3, 1)

Answer

(1, 5)

Question 6

Which of the following is a transformation that maps a figure onto itself?

Accepted Answer

Identity transformation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 7

Which transformation moves a figure in a straight line by a certain distance and in a certain direction?

Accepted Answer

Translation

Answer

Rotation about a fixed point

Answer

Reflection over a line

Question 8

A reflection across the y-axis is also commonly referred to as a:

Accepted Answer

Vertical reflection

Answer

Horizontal reflection

Answer

Diagonal reflection

Answer

Perpendicular reflection

Question 9

If a figure is reflected across two perpendicular lines, what is the resulting transformation?

Accepted Answer

Glide reflection

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 10

A regular hexagon has 6 lines of symmetry. After the hexagon is rotated 360 degrees around its center, how many lines of symmetry does it still have?

Accepted Answer

6

Answer

0

Answer

3

Question 11

To determine the possible transformations applicable to a figure, how can its symmetries be helpful?

Accepted Answer

Identifying axes or lines of symmetry

Answer

Determining the figure's perimeter

Answer

Counting the number of vertices

Question 12

What happens to the orientation of a figure after a 180-degree rotation around a point not at the origin?

Accepted Answer

Reverses

Answer

Remains the same

Answer

Depends on the figure's shape

Answer

Depends on the rotation direction

Question 13

Which type of transformation moves a figure up, down, left, or right without changing its size or shape?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Shear

Question 14

What transformation creates a mirror image of a figure across a line?

Accepted Answer

Reflection

Answer

Rotation

Answer

Translation

Question 15

What is the effect of a transformation with a scale factor of 1?

Accepted Answer

No change in the figure's size

Answer

Rotates the figure

Answer

Increases the figure's size

Answer

Decreases the figure's size

Question 16

Which transformation can map a figure onto itself without altering it in any way?

Accepted Answer

Identity transformation

Answer

Rotation

Answer

Translation

Question 17

A triangle has vertices at (2, 1), (5, 3), and (3, 4). If it is translated 3 units to the right and 2 units down, what are the coordinates of the new vertices?

Accepted Answer

(5, -1), (8, 1), (6, 2)

Answer

(-1, -1), (2, 1), (0, 2)

Answer

(2, -1), (5, 1), (3, 2)

Answer

(5, 1), (8, 3), (6, 4)

Question 18

Which transformation alters the size of a geometric figure?

Accepted Answer

Dilation

Answer

Reflection

Answer

Rotation

Answer

Translation

Question 19

A square is reflected across the y-axis. What is the relationship between the original square and its image?

Accepted Answer

The image is congruent to the original square.

Answer

The image is rotated 90 degrees from the original square.

Answer

The image is smaller than the original square.

Answer

The image is a rectangle.

Question 20

A point is rotated clockwise about the origin. If its image is located 180 degrees from its original position, what is the angle of rotation?

Accepted Answer

180 degrees

Answer

90 degrees

Answer

360 degrees

Answer

270 degrees

Question 21

A line segment with endpoints (1, 2) and (4, 6) is dilated by a scale factor of 2 with the origin as the center of dilation. What is the length of the image of the line segment?

Accepted Answer

10 units

Answer

5 units

Answer

20 units

Answer

2.5 units

Question 22

Which transformation is equivalent to a reflection over the x-axis followed by a reflection over the y-axis?

Accepted Answer

Rotation of 180 degrees about the origin

Answer

Reflection over the line y = x

Answer

Translation 2 units to the right

Answer

Dilation with a scale factor of -1

Question 23

A point is transformed using the rule (x, y) → (-y, x). What type of transformation is represented by this rule?

Accepted Answer

Rotation of 90 degrees counterclockwise about the origin

Answer

Reflection over the x-axis

Answer

Translation 1 unit to the left and 1 unit up

Question 24

Which of the following transformations does NOT preserve the orientation of a shape?

Accepted Answer

Reflection

Answer

Rotation

Answer

Dilation

Answer

Translation

Question 25

A triangle is transformed by a dilation with a scale factor of 1/2 followed by a translation 3 units up. How does the image relate to the original triangle?

Accepted Answer

The image is similar but not congruent to the original triangle.

Answer

The image is twice the size of the original triangle.

Answer

The image is congruent to the original triangle.

Question 26

What is the image of the point (-3, 5) after a reflection across the line y = x?

Accepted Answer

(5, -3)

Answer

(-5, 3)

Answer

(3, -5)