Free Printable Dilations Review

1.

Triangle CAT is formed by dilating triangle DOG. Which of the following is true?

a)

CAT ≅ DOG

b)

$\frac{CA}{DO}=\frac{AT}{OG}=\frac{TC}{GO}$

c)

CAT∼DOG

d)

∠C = ∠G

2.

A rectangular tin sign comes in three sizes, small, medium and large. All three have similar shapes. If the sides of the smallest sign are tripled to create the largest sign, which statement is true.

a)

The area of the largest sign is three times the area of the smaller sign.

b)

The perimeter of the larger sign is three times the perimeter of the smaller sign.

c)

The perimeter of the larger sign is nine times the perimeter of the smaller sign.

d)

The area of the smaller sign is nine times the area of the larger sign.

3.

Which transformation des NOT preserve congruence?

a)

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

b)

$(x,y)\ \rightarrow\ (x+4,y-1)$

c)

$(x,y)\ \rightarrow\ (4x,4y)$

d)

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

4.

Triangle ABC has coordinates A(2,8), B (4,6), C (6, -4). If ABC is dilated with the origin as the center of dilation to create triangle A'B'C', with coordinates A' (1,4), B'(2,3), and C'(3,-2), what is the rule of the dilation?

a)

$(x,y)\ \rightarrow\ (2x,2y)$

b)

$\left(x,y\right)\ \rightarrow\ \left(\frac{1}{2}x,\ y\right)$

c)

$\left(x,y\right)\ \rightarrow\ \left(x-1,\ y-4\right)$

d)

$\left(x,y\right)\ \rightarrow\ \left(\frac{1}{2}x,\ \frac{1}{2}y\right)$

5.

Triangle XYZ is transformed to create triangle X'Y'Z'. If the rule of the transformation is

$\left(x,y\right)\ \rightarrow\ \left(ax,\ ay\right)$ , which of the following is true?

a)

If $a<1$ , then the image of XYZ is larger than the pre-image.

b)

If $a=1$ , then the image of XYZ is larger than the pre-image.

c)

If $a>1$ , then the image of XYZ is smaller than the pre-image.

d)

If $a<1$ , then the image of XYZ is smaller than the pre-image.

6.

Triangle ABC has been reduced with P as the center of dilation to form triangle A'B'C'.

Which conclusion is correct?

a)

$\Delta A'B'C'\ \cong\ \Delta ABC$

b)

$\frac{AB}{A'B'}=\frac{BC}{B'C'}=\frac{CA}{C'A'}$

c)

$\frac{BC}{B'C'}=\frac{CA}{C'B'}=\frac{CB}{C'A'}$

d)

$A'A=B'B=C'C$

7.

Rectangle GHJK has coordinates (4, -2), (4,3), (2, -2) and (2,3). If GHJK is dilated with a scale factor of 7, which of the following coordinates could be from rectangle G'H'J'K'?

a)

(28, -28)

b)

(14, -14)

c)

(4, 21)

d)

(9, 10)

8.

If triangle ABC is transformed to triangle A'B'C' according to the rule $\left(x,y\right)\ \rightarrow\ \left(\frac{1}{4}x,\ \frac{1}{4}y\right)$ , which of the following is true?

a)

The angle measures of ABC are less than than the angle measures of triangle A'B'C'.

b)

The side lengths of ABC are $\frac{1}{4}$ as long as the side lengths of A'B'C'.

c)

The angle measures of A'B'C' are less than the angle measures of ABC.

d)

The side lengths of A'B'C' are $\frac{1}{4}$ as long as the side lengths of ABC.

9.

A transformation is applied 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 $90\degree\ clockwise$

10.

Triangle TRW was dilated using the origin as the center of dilation to create triangle XYZ. If a scale factor of 4 is used, what will be the value x-coordinate for point Z?

a)

12

b)

16

c)

4

d)

8

11.

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) $\rightarrow$ (ax,ay).

Which statement is 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 less than 1, the image of the polygon is smaller than the polygon.

12.

Quadrilateral LMPQ is shown on the coordinate grid. It will be dilated with the origin as the center of dilation using the rule (x, y) -> (ax, ay) to create quadrilateral L'M'P'Q'. If vertex P' will be located at (16.5, 5.5), what is the value of the scale factor a?

a)

$\frac{4}{11}$

b)

2.5

c)

2.75

d)

.5

13.

A triangle has vertices with coordinates (2,0), (3, -1) and (-2,-5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image?

a)

(5,3), (6,2), (1,-2)

b)

(6,0), (9,-3), (-6,-15)

c)

(2/3,0), (1,-1/3), (-2/3,-5/3)

d)

(-1,-3), (0,-4), (-5,-8)

14.

Click the picture. Then answer the question.

a)

$\left(x,y\right)\rightarrow\left(\frac{5}{7}x,\frac{5}{7}y\right)$

b)

$\left(x,y\right)\rightarrow\left(x+1,\ y+2\right)$

c)

$\left(x,y\right)\rightarrow\left(1.4x,1.4y\right)$

d)

$\left(x,y\right)\rightarrow\left(x-2,y+1\right)$

15.

Which of the following algebraic rules represents a dilation?

a)

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

b)

(x, y) --> (3x, 2y)

c)

(x, y) --> (x - 3, y + 5)

d)

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

e)

(x, y) --> (3x, 0.5y)

16.

Dilations have which operation?

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

17.

Which of the following algebraic rules represents a reduction?

a)

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

b)

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

c)

(x, y) --> (0.75x, 0.75y)

d)

(x, y) --> (0.999x, 0.999y)

e)

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

18.

Which of the following algebraic rules represents an enlargement?

a)

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

b)

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

c)

(x, y) --> (0.75x, 0.75y)

d)

(x, y) --> (0.999x, 0.999y)

e)

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

19.

State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor of 2.

a)

B' (2 , 4.5)

b)

B' (-8 ,-18)

c)

B' (8 ,18)

d)

B' (9 ,4)

20.

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

a)

½

b)

¼

c)

4

d)

2

21.

State the coordinate of the image of the given point B (-10,-6) under a dilation with center at the origin with the given scale factor k = 1/2.

a)

(5,3)

b)

(20,12)

c)

(-20,-12)

d)

(-5,-3)

Dilations Review

Total questions: 21

Worksheet time: 1hrs 3mins

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