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dilations and transformations

Total questions: 40

Worksheet time: 1hrs 14mins

Name

Class

Date

Which of the following describes the sequence of transformations shown?

Reflect across the x-axis and then rotate -90 degrees cw around the origin

Rotate 90 degrees cw around the origin and then translate down.

Reflect across the x-axis and then reflect across the y-axis.

Translate up and then rotate 90 degrees ccw about the origin.

Which rule shows the transformation?

(x, y) ----> (0.5x, 0.5y)

(x, y) ----> ( 2 + x, 2 + y)

(x, y) -----> (2x, 2y)

(x, y) -----> (3x, 3y)

The point (8, 12) was dilated to become point (2, 3). What was the scale factor?

What is the sequence of transformations?

Reflect over the y then reflect over the x

Reflect over the x then reflect over the y

Translate 4 units then rotate 90˚

Rotate 90˚ then reflect over the x

(2, 6) -- Translate up 3, left 1 and rotate 180°

(-1,-9)

(1, -9)

(5,5)

(-5,5)

(-3, -1) -- Reflect across the line y=x and translate down 1.

(-1, -4)

(-1, -2)

(3, 0)

(-2, -3)

Choose the correct transformations

rotate 90 degrees counter-clockwise around the origin, and then reflect over the x-axis

right 1, down 4, and then reflection over the y-axis

right 6, and then reflection over the x-axis

reflection over the line y=x, and then translate up 4, right 2

How is trapezoid ABCD translated to trapezoid A'B'C'D'?

(x + 5, y - 5) 5 units down and 5 units to the right

(x + 1, y - 5) 5 units down and 1 to the right

(x + 5, y - 8) 8 units down and 5 units to the right

(x + 4, y - 5) 5 units down and 4 units to the right

What does a translation do to an image?

Turns it 90* clockwise

Mirrors it

Shrinks it

Slides it

10.

Reflections over the x-axis change the ____-__________.

y-coordinate

x-coordinate

y-axis

x-axis

11.

Reflecting over the y-axis changes the ____-_____________.

x-axis

x-coordinate

y-coordinate

none of the above

12.

Which algebraic rule shows how triangle ABC being translated to triangle A'B'C'?

(x, y) --> (x - 3, y + 8)

(x, y) --> (x + 3, y - 8)

(x, y) --> (x - 4, y + 9)

(x, y) --> (x + 4, y - 9)

13.

Triangle ABC is labeled with points A(5, 2), B(1, 2) and C(3, 6) on a coordinate plane. Find the coordinates of A' B' C' after a reflection over the x-axis.

A’(5, -2) B' (1, -2) C' (3, -6)

A’(-5, -2) B' (-1, -2) C' (-3, -6)

A’(-5, -2) B' (-2, -1) C' (-6, -3)

14.

A transformation that “turns” a figure about a fixed point at a given angle and a given direction.

reflection

translation

rotation

dilation

15.

A type of transformation where a figure is “flipped” over a line of symmetry. A reflection produces a mirror image of a figure.

rotation

translation

dilation

reflection

16.

A type of transformation where a geometric figure slides horizontally, vertically, or both. What type of transformation is this?

dilation

translation

rotation

reflection

17.

When you translate
(x , y + 6) the figure will move _____.

6 units right

6 units left

6 units up

6 units down

18.

When you translate,
(x - 4, y) the figure will move _____.

4 units right

4 units left

4 units up

4 units down

19.

Going from (x,y) to (-x,-y) will result in a counter-clockwise rotation of _____ degrees.

180

270

360

20.

Which rule would result in a translation of 2 units left and 3 units up?

(x, y) → (2x, 3y)

(x, y) → (x - 2, y + 3)

(x, y) → (-x, -y)

(x, y) → (x + 2, y - 3)

21.

Identify the transformation from ABC to A'B'C'. (scale on graph is 1)

(x+8, y+4)

(x-8, y-4)

(x+4, y+8)

(x-4, y-8)

22.

Identify the transformation from B to D.

90^o Clockwise Rotation

180^o Rotation

270^o clockwise Rotation

360^o Rotation

23.

Does the transformation shown preserve congruence and/or orientation?

Congruence yes, Orientation yes

Congruence No, Orientation No

Congruence No, Orientation yes

Congruence Yes, Orientation No

24.

Does the transformation shown preserve congruence and/or orientation?

Congruence yes, Orientation yes

Congruence no, Orientation no

Congruence yes, Orientation no

Congruence no, Orientation yes

25.

What is the rule for the following reflection?

Reflection across the x-axis (x, -y)

Reflection across the y-axis (-x, y)

26.

Choose the correct scale factor:

1/3

1/2

27.

Dilate Point B by a scale factor of 1/2

(1.5,-4)

(-1.5,1)

(-1,-1.5)

(-2,-2)

28.

When A(3, 6) is under a dilation of 2 what are the coordinates of A'?

(3, 6)

(1.5, 3)

(6, 12)

(12, 6)

29.

What Transformation is visible?

Reflection

Translation

Rotation

Dilation

30.

Triangle EFG is dilated with a scale factor of 1/2. The measure of <F is 36 degrees. What is m<F' ?

31.

A triangle is dilated with a center of dilation at the origin. Point P is on the figure and P' is the corresponding point on the image of the dilation. Point P is at (-2,3) and P' is at (-8,12). What is the scale factor?

32.

What is the length of BC?

6 2/3 cm

5 cm

4 cm

6 cm

33.

Triangle ABC is dilated to produce A'B'C' with a scale factor of 3/4. Which describes the relationship between the two triangles?

A'B'C' is an enlargement

A'B'C' is a reduction

A'B'C' is congruent to ABC

A'B'C' is a mirror image of ABC

34.

A triangle has vertices at (1,1), (1,2), and (3,2). It is dilated by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?

(4,1) (4,2) (6,2)

(1,4) (1,5) (3,5)

(3,3) (3,6) (9,6)

35.

Which rule would result in a translation of 2 units left and 3 units up?

(x, y) → (2x, 3y)

(x, y) → (x - 2, y + 3)

(x, y) → (-x, -y)

(x, y) → (x + 2, y - 3)

36.

Given the triangles are similar. Which is the length of UV?

3.6 inches

2.4 inches

8.1 inches

4 inches

37.

Which of the following are true about dilations? Select all that apply.

Dilations have the same shape as the original.

Dilations can be enlargements of the original image.

Dilations can be reductions of the original image.

Dilations are always congruent.

38.

Rectangle ABCD is dilated to form rectangle A'B'C'D'.

What is the scale factor?

1/2

(1,2)

(2,1)

39.

Suppose <G=<S, <R=<T, <M=<N.

Which statement is correct? Select all that apply.

The sides are proportional

The sides are congruent

GRM is similar to NST

MGR is congruent to NST

40.

Write a rule for the translation.

(x -1, y + 2)

(x -2, y + 1)

(x +2, y - 1)

(x +1, y - 2)

Reset

dilations and transformations

Total questions: 40

Worksheet time: 1hrs 14mins

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