Free Printable Similar Figures and Transformations

1.

Figure I and Figure II are similar figures. Which proportion must be true?

a)

b)

c)

d)

2.

Which algebraic expression represents a dilation?

a)

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

b)

(x,y)->(x+5,y-8)

c)

(x,y)->(5x,5y)

d)

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

3.

Which algebraic expression represents a rotation of 90/270?

a)

(x,y) $\rightarrow$ (y,-x)

b)

(x,y) $\rightarrow$ (-x,-y)

c)

(x,y) $\rightarrow$ (y,x)

d)

(x,y) $\rightarrow$ (x+6,y+3)

4.

Write a rule for the translation.

a)

(x -1, y + 2)

b)

(x -2, y + 1)

c)

(x +2, y - 1)

d)

(x +1, y - 2)

5.

The pair of figures is similar. Find the missing side.

a)

x = 12

b)

x = 3

c)

x = 40

d)

x = 4

6.

What is the scale factor of the dilation?

a)

5/2

b)

3/2

c)

7/2

d)

2/3

7.

Choose the correct scale factor:

a)

2

b)

3

c)

1/3

d)

1/2

8.

How can this transformation be represented algebraically?

a)

(x + 4, y)

b)

(-x, -y)

c)

(-x, y)

d)

(y, -x)

9.

In a dilation what mathematical operation is used with the scale factor?

a)

addition

b)

subtraction

c)

multiplication

d)

division

10.

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

a)

Translated 5 units down and 5 units to the right

b)

Translated 5 units down and 1 to the right

c)

Translated 8 units down and 5 units to the right

d)

Translated 5 units down and 4 units to the right

11.

What is the algebraic rule?

a)

A

b)

B

c)

C

d)

D

12.

Find the measure of x:

a)

6

b)

24

c)

33

d)

36

13.

A polygon will be dilated on a coordinate grid to create a larger polygon. The polygon is dilated using the origin as the center of dilation.
Which rule could represent this dilation?

a)

(x,y) → (0.5 − x,0.5 − y)

b)

(x,y) → (x−7,y−7)

c)

(x,y)→( $\frac{5}{4}$ x, $\frac{5}{4}$ y)

d)

(x, y) → (0.9x, 0.9y)

14.

Triangle ABC was transformed to create triangle A′B′C′. Which rule best describes this transformation?

a)

(x,y)→(x,y−7)

b)

(x, y) → (x, −y)

c)

(x,y)→(x−7,y)

d)

(x, y) → (−x, y)

15.

Quadrilateral KMPT is dilated by a scale factor of $\frac{3}{4}$ to create quadrilateral K′M′P′T′. The perimeter of quadrilateral KMPT is x units.
What is the perimeter in units of quadrilateral K′M′P′T′?

a)

x units

b)

$\frac{3}{4}$ x units

c)

$\left(\frac{3}{4}\right)^2$ x units

d)

$\frac{4}{3}$ x units

16.

A polygon is graphed on a coordinate grid with (x, y) representing the location of a certain point on the polygon. The polygon is transformed using the rule (x, y) → (ax, ay).

Which statement must be true?

a)

If a is greater than 1, the image of the polygon is congruent to the polygon.

b)

If a is between 0 and 1, the image of the polygon is congruent to the polygon.

c)

If a is greater than 1, the image of the polygon is smaller than the polygon.

d)

If a is between 0 and 1, the image of the polygon is smaller than the polygon.

17.

Quadrilateral PQRS was translated 5 units to the right and 3 units up to create quadrilateral P′Q′R′S′. Which rule describes this transformation?

a)

(x,y) → (x−5,y−3)

b)

(x,y) → (x+5,y+3)

c)

(x,y) → (x−3,y−5)

d)

(x,y) → (x+3,y+5)

18.

Figure I and Figure II are similar pentagons. Which proportion must be true?

a)

b)

c)

d)

19.

Quadrilateral PRST is transformed according to the rule (x, y) → (x + 9, y + 4) to create quadrilateral P′R′S′T′. Which statement is true?

a)

The side lengths of quadrilateral P′R′S′T′ are twice the corresponding side lengths of quadrilateral PRST.

b)

The angle measures of quadrilateral P′R′S′T′ are equal to the corresponding angle measures of quadrilateral PRST.

c)

The side lengths of quadrilateral P′R′S′T′ are 9 units longer than the corresponding side lengths of quadrilateral PRST.

d)

The angle measures of quadrilateral P′R′S′T′ are greater than the corresponding angle measures of quadrilateral PRST.

20.

A transformation is applied to a figure to create a new figure. Which transformation does not preserve congruence?

a)

A reflection across the x-axis

b)

A translation 7 units down

c)

A dilation by a scale factor of 5

d)

A rotation of 90° clockwise

Similar Figures and Transformations

Total questions: 20

Worksheet time: 51mins

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