Geometry Transformations: Master the Art of Shape Manipulation

Question 1

Which transformation alters the size of a shape?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 2

Which of the following is NOT a type of geometric transformation?

Accepted Answer

Stretching

Answer

Rotation

Answer

Reflection

Answer

Translation

Question 3

When a shape is translated 5 units to the right, what are the coordinates of its new image?

Accepted Answer

(x + 5, y)

Answer

(y + 5, x)

Answer

(x - 5, y)

Answer

(x, y + 5)

Question 4

What is the center of rotation when a shape is rotated 180 degrees about the y-axis?

Accepted Answer

The origin (0,0)

Answer

The y-intercept

Answer

The x-axis

Answer

The midpoint of the line segment connecting the shape's endpoints

Question 5

What is the scale factor when a shape is dilated by a factor of 3?

Accepted Answer

3

Answer

1/3

Answer

2

Answer

1/2

Question 6

Which of the following sequences of transformations will result in a shape that is congruent to the original?

Accepted Answer

Translation, rotation, and translation

Answer

Reflection, rotation, and dilation

Answer

Translation, dilation, and reflection

Answer

Dilation, reflection, and translation

Question 7

What is the image of the point (2, 5) after a reflection over the x-axis?

Accepted Answer

(2, -5)

Answer

(-2, 5)

Answer

(2, 5)

Answer

(-2, -5)

Question 8

Which of the following transformations will produce an image that is smaller than the original?

Accepted Answer

Dilation with a scale factor less than 1

Answer

Rotation

Answer

Reflection

Answer

Translation

Question 9

Which of the following is an application of transformations in real-world scenarios?

Accepted Answer

Creating blueprints for buildings

Answer

Solving algebraic equations

Answer

Translating languages

Answer

Writing computer programs

Question 10

What transformation moves a figure horizontally?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 11

Which transformation creates a flipped image of a figure over a line?

Accepted Answer

Reflection

Answer

Rotation

Answer

Translation

Answer

Dilation

Question 12

What transformation involves turning a figure around a fixed point?

Accepted Answer

Rotation

Answer

Dilation

Answer

Translation

Answer

Reflection

Question 13

Which transformation changes the size of a figure without changing its shape?

Accepted Answer

Dilation

Answer

Rotation

Answer

Translation

Question 14

A rectangle is translated 4 units to the right. What are the coordinates of its new vertices?

Accepted Answer

(x + 4, y)

Answer

(x, y - 4)

Answer

(x, y + 4)

Answer

(x - 4, y)

Question 15

A circle is rotated 180 degrees clockwise around its center. What is the orientation of the circle now?

Accepted Answer

Rotated 180 degrees clockwise

Answer

Translated

Answer

Reflected

Answer

Rotated 180 degrees counterclockwise

Question 16

A figure is reflected over the x-axis. What is the effect on its y-coordinates?

Accepted Answer

They change sign.

Answer

They remain the same.

Answer

They double.

Answer

They halve.

Question 17

A triangle is dilated by a scale factor of 3. What is the ratio of the perimeter of the dilated triangle to the original triangle?

Accepted Answer

3

Answer

1

Answer

1/3

Answer

9

Question 18

Which of the following is NOT a type of geometric transformation that preserves the shape of a figure?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 19

What is the rule for translating a shape 3 units up and 5 units to the right?

Accepted Answer

(x, y) → (x + 5, y + 3)

Answer

(x, y) → (x - 5, y)

Answer

(x, y) → (x, y - 5)

Answer

(x, y) → (x, y + 5)

Question 20

What is the scale factor for a shape that has been dilated by a factor of 1/2?

Accepted Answer

1/2

Answer

2

Answer

3

Answer

4

Question 21

What is the image of the line y = x under the rotation 90 degrees clockwise about the origin?

Accepted Answer

y = -x

Answer

y = -1/2x

Answer

x = y

Answer

y = 2x

Question 22

Which transformation moves a shape without changing its size or how it's facing?

Accepted Answer

Translation

Answer

Reflection

Answer

Rotation

Answer

Dilation

Question 23

If you flip point A (2, 3) over the y-axis, what are its new coordinates (A')?

Accepted Answer

(-2, 3)

Answer

(-2, -3)

Answer

(2, -3)

Answer

(3, 2)

Question 24

A triangle is spun 90 degrees clockwise around the origin. What's the relationship between the original triangle and the new one?

Accepted Answer

The new triangle is exactly the same size and shape as the original.

Answer

The new triangle is neither the same size nor the same shape.

Answer

The new triangle is similar but bigger.

Answer

The new triangle is similar but smaller.

Question 25

Which transformation can make a shape bigger or smaller?

Accepted Answer

Dilation

Answer

Translation

Answer

Reflection

Answer

Rotation

Question 26

A shape is moved 3 units to the right and 2 units down.  Which rule describes this move?

Accepted Answer

(x, y) → (x + 3, y - 2)

Answer

(x, y) → (x - 3, y + 2)

Answer

(x, y) → (x - 2, y + 3)

Answer

(x, y) → (x + 2, y - 3)

Question 27

You shrink a rectangle by a factor of 1/2.  How does the area of the new rectangle compare to the original?

Accepted Answer

The new rectangle's area is one-fourth the size of the original.

Answer

The new rectangle's area is half as big.

Answer

The new rectangle's area is twice as big.

Question 28

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

Accepted Answer

(0, 2)

Answer

(0, 6)

Answer

(3, 2)

Answer

(6, 6)

Question 29

A square has a side length of 4 units. If it is rotated 90 degrees clockwise around its center, what is the side length of the resulting square?

Accepted Answer

4

Answer

16

Answer

2

Answer

8

Question 30

A rectangle is reflected across the y-axis. What happens to the x-coordinates of its vertices?

Accepted Answer

They change sign.

Answer

They double.

Answer

They remain the same.

Answer

They are halved.

Question 31

A triangle has side lengths of 3, 4, and 5 units. It is dilated by a scale factor of 2. What is the perimeter of the resulting triangle?

Accepted Answer

24

Answer

12

Answer

60

Answer

36

Question 32

Which of these transformations *doesn't* keep the orientation of a figure the same?

Accepted Answer

Reflection

Answer

Dilation

Answer

Translation

Answer

Rotation

Question 33

A circle has its center at (2, 3) and a radius of 5 units. If it is translated 4 units to the right and 1 unit up, what are the coordinates of the new center?

Accepted Answer

(6, 4)

Answer

(6, 3)

Answer

(2, 4)

Question 34

A square has vertices at (1, 1), (1, 3), (3, 3), and (3, 1). If it is reflected across the line y = x, what are the coordinates of the image of the vertex (1, 3)?

Accepted Answer

(3, 1)

Answer

(3, 3)

Answer

(-1, 3)

Answer

(1, -3)

Question 35

A triangle is dilated by a scale factor of 1/2. What is the ratio of the area of the smaller triangle to the area of the original triangle?

Accepted Answer

1/4

Answer

1

Answer

1/2

Answer

4

Question 36

A figure is rotated 180 degrees about the origin. What happens to the coordinates of its vertices?

Accepted Answer

Both x and y coordinates change sign.

Answer

The coordinates remain the same.

Answer

Only the x coordinates change sign.

Answer

Only the y coordinates change sign.

Question 37

A rectangle is dilated with a scale factor of 3. How does the perimeter of the new rectangle compare to the perimeter of the original rectangle?

Accepted Answer

It is tripled.

Answer

It is doubled.

Answer

It remains the same.

Answer

It is multiplied by 9.

Question 38

Which transformation slides every point of a figure the same distance in the same direction?

Accepted Answer

Translation

Answer

Rotation

Answer

Dilation

Answer

Reflection

Question 39

If you reflect a triangle across the y-axis, what happens to its size and shape?

Accepted Answer

The image is the same size and shape as the original triangle.

Answer

The image is a different shape than the original triangle.

Answer

The image is smaller than the original triangle.

Answer

The image is larger than the original triangle.

Question 40

Rotating a point 90 degrees clockwise is the same as rotating it how many degrees counterclockwise?

Accepted Answer

270 degrees

Answer

360 degrees

Answer

180 degrees

Answer

90 degrees

Question 41

If you enlarge a square by a scale factor of 2, how much bigger does the area become?

Accepted Answer

Four times bigger

Answer

Twice as big

Answer

Half the size

Answer

The same size

Question 42

To move Figure A onto Figure B, what transformations could you use?

Accepted Answer

Reflect across the x-axis, then slide 3 units to the right.

Answer

Rotate 90 degrees clockwise, then slide 3 units down.

Answer

Double the size, then reflect across the y-axis.

Question 43

A line segment has endpoints (2, 4) and (6, 8). If you move it 3 units down and 2 units to the left, what are the new endpoints?

Accepted Answer

(0, 1) and (4, 5)

Answer

(0, 7) and (4, 11)

Answer

(4, 7) and (8, 11)

Answer

(2, 1) and (6, 5)

Question 44

Which of these transformations changes the size of a figure?

Accepted Answer

Dilation

Answer

Rotation

Answer

Reflection

Answer

Translation

Question 45

If you rotate a triangle 180 degrees around the origin, and point A starts at (3, -2), where will point A' end up?

Accepted Answer

(-3, 2)

Answer

(3, 2)

Answer

(-2, 3)

Question 46

If you shrink a triangle by a scale factor of 1/3, what's true about the new triangle?

Accepted Answer

It's the same shape but smaller.

Answer

It's the same shape but bigger.

Answer

It's exactly the same size and shape.

Question 47

Which transformation keeps a figure looking exactly the same?

Accepted Answer

Rotating it a full circle (360 degrees)

Answer

Sliding it 5 units to the right

Answer

Making it twice as big

Answer

Flipping it across the y-axis