Question 1

If ∆ABC is dilated by a scale factor of 3, which statement is true of the image ∆A'B'C'?

Accepted Answer

B'C' = 3BC

Answer

m<A' = 3(m<A)

Answer

3(m<C') = m<C

Answer

3A'B' = AB

Question 2

In the diagram, CD is the image of AB after a dilation of scale
factor k with center E.  Which ratio is equal to the scale factor k of the dilation?

Accepted Answer

$\frac{EC}{EA}$

Answer

$\frac{BA}{EA}$

Answer

$\frac{EA}{BA}$

Answer

$\frac{EA}{EC}$

Question 3

The image of ∆ABC after a dilation of scale factor k centered at point A is ∆ADE, as shown in the diagram.  Which statement is always true?

Accepted Answer

BC || DE

Answer

AC = CE

Answer

2AB = AD

Answer

AD $\perp$DE

Question 4

In the diagram, ∆ABC ~ ∆ADE.  Which measurements are justified by this similarity?

Accepted Answer

AD = 2, AB = 6, AE = 5, and AC = 15

Answer

AD = 3, AB = 9, AE = 5, and AC = 10

Answer

AD = 5, AB = 8, AE = 7, and AC = 10

Answer

AD = 3, AB = 6, AE = 4, and AC = 12

Question 5

A triangle is dilated by a scale factor of 3 with the center of dilation at the origin. Which statement is true?

Accepted Answer

The area of the image is nine times the area of the original triangle.

Answer

The perimeter of the image is nine times the perimeter of the original triangle.

Answer

The measure of each angle in the image is three times the measure of the corresponding angle of the original triangle.

Answer

The slope of any side of the image is three times the slope of the corresponding side of the original triangle.

Question 6

In the diagram, ∆ABE is the image of ∆ACD after a dilation centered at the origin.  The ratio of the lengths of BE to CD is

Accepted Answer

2/3

Answer

3/4

Answer

4/3

Answer

3/2

Question 7

The line 3y = -2x + 8 is transformed by a dilation centered at the origin. Which linear equation could be its image?

Accepted Answer

2x + 3y = 5

Answer

3x - 2y = 5

Answer

2x - 3y = 5

Answer

3x + 2y = 5

Question 8

The line whose equation is y = 3x - 1 is transformed by a dilation with a scale factor of 2 and centered at (3,8). The line’s image is

Accepted Answer

y = 3x - 1

Answer

y = 3x - 4

Answer

y = 3x - 2

Answer

y = 3x - 8

Question 9

A three-inch line segment is dilated by a scale factor of 6 and centered at its midpoint. What is the length of its image?

Accepted Answer

18 inches

Answer

9 inches

Answer

15 inches

Answer

2 inches

Question 10

In the diagram, ∆A'B'C' is the image of ∆ABC after a dilation centered at the origin. What is the scale factor?

Accepted Answer

2.5

Question 11

In the diagram, FE $\perp$ CE.  What is a correct sequence of similarity transformations that proves ∆ABC ~ ∆DEF?

Accepted Answer

a counterclockwise rotation of 90 degrees about point E followed by a dilation with a scale factor of 2 centered at point E

Answer

a rotation of 180 degrees about point E followed by a horizontal translation

Answer

a counterclockwise rotation of 90 degrees about point E followed by a horizontal translation

Answer

a rotation of 180 degrees about point E followed by a dilation with a scale factor of 2 centered at point E

Question 12

Line segment A'B', whose endpoints are (4,-2) and (16,14), is the image of segment AB after a dilation of 1/2 centered at the origin.  What is the length of AB?
(1) 5 (3) 20
(2) 10 (4) 40

Accepted Answer

40

Answer

20

Answer

10

Answer

5

Question 13

In the diagram, ∆ADE is the image of ∆ABC after a reflection over the line AC followed by a dilation of scale factor $\frac{AE}{AC}$centered
at point A.  Which statement must be true?

Accepted Answer

m∠ABC = m∠ADE

Answer

m∠BAC = m∠AED

Answer

m∠ACB = $\frac{1}{2}$ m∠DAB

Answer

m∠DAE = $\frac{1}{2}$ m∠BAC

Question 14

What are the coordinates of B'and C' after BC undergoes a dilation centered at point A with a scale factor of 2?

Accepted Answer

B'(5,2) and C'(1,-2)

Answer

B'(5,0) and C'(1,-2)

Answer

B'(5,2) and C'(3,0)

Answer

B'(6,1) and C'(0,-1)

Question 15

A line segment is dilated by a scale factor of 2 centered at a point not on the line segment. Which statement regarding the relationship between the given line segment and its image is true?

Accepted Answer

The line segments are parallel, and the image is twice the length of the given line segment.

Answer

The line segments are perpendicular, and the image is twice the length of the given line segment.

Answer

The line segments are parallel, and the image is one-half the length of the given line segment.

Answer

The line segments are perpendicular, and the image is one-half the length of the given line segment.

Question 16

Line n is represented by the equation 3x + 4y = 20. What is the equation of line p, the image of line n, after a dilation of scale factor $\frac{1}{3}$ centered at the point (4,2)?

Accepted Answer

3x + 4y = 20

Answer

y = $\frac{1}{3}$x + 4

Answer

y = $\frac{1}{3}$x - 2

Answer

3x + 4y = 8

Question 17

The line represented by the equation 4y = 3x + 7 is transformed by a dilation centered at the origin. Which linear equation could represent its image?

Accepted Answer

3x - 4y = 9

Answer

4x + 3y = 9

Answer

3x + 4y = 9

Answer

4x - 3y = 9

Question 18

Rectangle A'B'C'D' is the image of rectangle ABCD after a dilation centered at point A by a scale factor of $\frac{2}{3}$ . Which statement is correct?

Accepted Answer

Rectangle A'B'C'D' has a perimeter that is $\frac{2}{3}$ the perimeter of rectangle ABCD.

Answer

Rectangle A'B'C'D' has an area that is $\frac{3}{2}$ the perimeter of rectangle ABCD.

Answer

Rectangle A'B'C'D' has an area that is $\frac{2}{3}$ the perimeter of rectangle ABCD.

Answer

Rectangle A'B'C'D' has a perimeter that is $\frac{3}{2}$ the perimeter of rectangle ABCD.

Question 19

The line whose equation is 3x - 5y = 4 is dilated by a scale factor
of $\frac{5}{3}$ centered at the origin. Which statement is correct?

Accepted Answer

The image of the line has the same slope as the pre-image but a different y-intercept.

Answer

The image of the line has the same y-intercept as the pre-image but a different slope.

Answer

The image of the line has the same slope and the same y-intercept as the pre-image.

Answer

The image of the line has a different slope and a different y-intercept from the pre-image.

Question 20

In the diagram, two concentric circles with center O, and radii OC, OD, OCE, and ODF are drawn.  If OC = 4 and OE = 6, which relationship between the length of arc EF and the length of arc CD is always true?

Accepted Answer

The length of arc EF is 1.5 times the length of arc CD.

Answer

The length of arc EF is 2 times the length of arc CD.

Answer

The length of arc EF is 2 units longer than the length of arc CD.

Answer

The length of arc EF is 4 units longer than the length of arc CD.

Question 21

Triangle ABC is the image of triangle ADE after a dilation centered at A.  What is the scale factor of the dilation?

Accepted Answer

$\frac{1}{3}$

Answer

$\frac{1}{2}$

Answer

3

Answer

2

Question 22

Given square RSTV, where RS = 9. If square RSTV is dilated by a scale factor of 3 about a given center, what is the perimeter of the image of RSTV after the dilation?

Accepted Answer

108

Answer

27

Answer

12

Answer

36

Question 23

Line MN is dilated by a scale factor of 2 centered at the point (0,6). If MN is represented by y = -3x + 6, which equation can representM'N', the image of MN ?

Accepted Answer

y = -3x + 6

Answer

y = -3x + 12

Answer

y = -6x + 12

Answer

y = -6x + 6

Question 24

Triangle RJM has an area of 6 and a perimeter of 12. If the triangle is dilated by a scale factor of 3 centered at the origin, what are the area and perimeter of its image, triangle R'J'M'?

Accepted Answer

area of 54 and perimeter of 36

Answer

area of 9 and perimeter of 15

Answer

area of 18 and perimeter of 36

Answer

area of 54 and perimeter of 108

Question 25

The line whose equation is 4x + 3y = 24 is dilated by a scale factor of 2 centered at (3, 4).  What is true about the image of the line?

Accepted Answer

It is the same as the original line

Answer

It has a different slope and y-intercept than the original line

Answer

It has a different slope than the original line but the same y-intercept

Answer

It has the same slope as the original line but a different y-intercept.

Question 26

After a dilation with center (0,0), the image of DB is D'B'. If DB = 4.5 and D'B' = 18, the scale factor of this dilation is

Accepted Answer

4

Answer

$\frac{1}{4}$

Answer

5

Answer

$\frac{1}{5}$

Question 27

Which sequence of transformations will map ∆ABC onto ∆DEF?

Accepted Answer

a dilation of ∆ABC by a scale factor of 2 centered at the origin,
followed by a rotation of 180° about the origin

Answer

a dilation of ∆ABC by a scale factor of 2 centered at the origin

Answer

a dilation of ∆ABC by a scale factor of 1/2 centered at the origin,
followed by a rotation of 180° about the origin

Answer

a dilation of ∆ABC by a scale factor of 1/2 centered at the origin

Question 28

What is an equation of the image of the line y = $\frac{3}{2}$x - 4 after a dilation of a scale factor of $\frac{3}{4}$ centered at the origin?

Accepted Answer

y = $\frac{3}{2}$x - 3

Answer

y = $\frac{3}{2}$x - 4

Answer

y = $\frac{9}{8}$x - 3

Answer

y = $\frac{9}{8}$x - 4

Question 29

After a dilation centered at the origin, the image of CD is C'D'.
If the coordinates of the endpoints of these segments are C(6,-4), D(2,-8), C'(9,-6), and D'(3,-12), the scale factor of the dilation is

Accepted Answer

$\frac{3}{2}$

Answer

3

Answer

$\frac{2}{3}$

Answer

$\frac{1}{3}$

Question 30

The line -3x + 4y = 8 is transformed by a dilation centered at the origin. Which linear equation could represent its image?

Accepted Answer

y = $\frac{3}{4}$x + 8

Answer

y = -$\frac{3}{4}$x - 8

Answer

y = -$\frac{4}{3}$x - 8

Answer

y = $\frac{4}{3}$x + 8

Question 31

On the set of axes, AB is dilated by a scale factor of 5/2 centered at point P.  Which statement is always true?

Accepted Answer

AB || A'B'

Answer

AB = A'B'

Answer

PA = AA'

Answer

$\frac{5}{2}$(A'B') = AB

Question 32

The line represented by 2y = x + 8 is dilated by a scale factor
of k centered at the origin, such that the image of the line has an
equation of y - $\frac{1}{2}$x = 2. What is the scale factor, k?

Accepted Answer

1/2

Answer

4

Answer

1/4

Answer

2

Question 33

In the diagram, EB || DC.  What is the length of AC, to the nearest tenth?

Accepted Answer

14.3

Answer

5.1

Answer

5.2

Answer

14.4

Question 34

If AB = 9, BC = 15, DE = 6, EF = 10, and ∠B $\cong$∠E, which statement is true?

Accepted Answer

∆ABC ~ ∆DEF

Answer

$\frac{AB}{DE}$ = $\frac{FE}{CB}$

Answer

<CAB $\cong$ <DEF

Answer

$\frac{AB}{CD}$ = $\frac{FE}{DE}$

Question 35

In the diagram of right triangle ABC, CD is the altitude drawn to the hypotenuse AB. Which lengths would NOT produce an altitude with length 6$\sqrt{2}$?

Accepted Answer

AD = 3 and AB = 24

Answer

AD = 2 and DB = 36

Answer

AD =8 and AB = 17

Answer

AD = 6 and DB = 12

Question 36

In the diagram, AC || BD.  Which equation is true?

Accepted Answer

$\frac{AE}{BE}$ = $\frac{AC}{BD}

Answer

$\frac{CA}{DB}$ = $\frac{ED}{EC}

Answer

$\frac{CE}{DE}$ = $\frac{EB}{EA}

Answer

$\frac{CE}{AE}$ = $\frac{EB}{ED}

Question 37

In the diagram, ∆ABC ~ ∆DEC.  If AC = 12, DC = 7, DE = 5, and the perimeter of ∆ABC is 30, what is the perimeter of ∆DEC?

Accepted Answer

17.5

Answer

14.0

Answer

12.5

Answer

14.8

Question 38

To find the distance across a pond from point B to point C, a surveyor drew the diagram below. The measurements he made are indicated on his diagram.  Use the surveyor’s information to determine and state the distance from point B to point C, to the nearest yard.

Accepted Answer

164

Question 39

The ratio of similarity of ∆BOY to ∆GRL is 1:2. If BO = x + 3 and GR = 3x - 1, then the length of GR is

Accepted Answer

20

Answer

10

Answer

7

Answer

5

Question 40

In ∆SCU, segment OT is drawn so that ∠C $\cong$ ∠OTU.  If TU = 4, OU = 5, and OC = 7, what is the length of ST?

Accepted Answer

11

Answer

8.75

Answer

5.6

Answer

15

Question 41

In ∆RST shown, altitude SU is drawn to hypotenuse RT at U.  If UT = 12 and RT = 42, what is the value of h?

Accepted Answer

6$\sqrt{10}$

Answer

6$\sqrt{2}$

Answer

6$\sqrt{35}$

Answer

6$\sqrt{14}$

Question 42

In the diagram, AC || DE.  If AD = 24, DB = 12, DE = 4, the length of AC is

Accepted Answer

12

Answer

8

Answer

72

Answer

16

Question 43

In right triangle ABC, altitude CD is drawn to hypotenuse AB.  If AD = 4 and DB = 6, what is the length of AC?

Accepted Answer

2$\sqrt{10}$

Answer

2$\sqrt{6}$

Answer

2$\sqrt{15}$

Answer

4$\sqrt{2}$

Question 44

In the diagram, <H $\cong$ <RDO.  If RD = 4, RO = 6, and OH = 4, the length of CD is

Accepted Answer

11

Answer

2$\frac{2}{3}$

Answer

6$\frac{2}{3}$

Answer

15

Question 45

Given ∆MRO shown with trapezoid PTRO, MR = 9, MP = 2, and PO = 4.  What is the length of TR?

Accepted Answer

6

Answer

4.5

Answer

3

Answer

5

Question 46

In the diagram, AB || DE.  If CD = 6.6,  DE = 3.4, CE = 4.2, and BC = 5.25, what is the length of AC, to the nearest hundredth?

Accepted Answer

8.25

Answer

2.70

Answer

5.28

Answer

3.34

Question 47

In the diagram, BE || CD.  What is the length of AE, to the nearest tenth?

Accepted Answer

4.0

Answer

14.0

Answer

3.3

Answer

5.1

Question 48

In the diagram, KM = 16.  Which lengths would make triangle KLM a right triangle with altitude LN?

Accepted Answer

LM = 12 and NM = 9

Answer

KL = 11 and KN = 7

Answer

LM = 13 and KN = 6

Answer

LN = 8 and NM = 10

Question 49

In the diagram, DE || AB.  The length of DE is

Accepted Answer

25

Answer

15

Answer

30

Answer

24

Question 50

The line whose equation is 3x - 5y = 4 is dilated by a scale factor of 2 centered at the origin. Which statement is correct?

Accepted Answer

The image of the line has the same slope as the pre-image but a different y-intercept.

Answer

The image of the line has a different slope and a different y-intercept from the pre-image.

Answer

The image of the line has the same slope and the same y-intercept as the pre-image.

Answer

The image of the line has the same y-intercept as the pre-image but a different slope.

Question 51

What is the length of BC?

Accepted Answer

4$\sqrt{3}$

Answer

4$\sqrt{5}$

Answer

4$\sqrt{6}$

Answer

4$\sqrt{2}$

Question 52

In the diagram, what is the length of CB?

Accepted Answer

16.2

Answer

3.2

Answer

19.2

Answer

4.8

Question 53

In the diagram, DE || BC.  Which statement is always true?

Accepted Answer

$\frac{AB}{AD}$ = $\frac{BC}{DE}$

Answer

$\frac{DE}{BC}$ = $\frac{DB}{AC}$

Answer

$\frac{AC}{BC}$ = $\frac{DE}{AE}$

Answer

$\frac{AC}{CE}$ = $\frac{BC}{DE}$

Question 54

In the diagram, ST || PR.  What is the length of QR ?

Accepted Answer

17.5

Answer

12.5

Answer

7

Answer

2

Question 55

Line segment CD is the altitude drawn to hypotenuse EF in right triangle ECF. If EC = 10 and EF =􏰁 24, then, to the nearest tenth, ED is

Accepted Answer

4.2

Answer

15.5

Answer

21.8

Answer

5.4

Question 56

In the diagram below of right triangle ABC, altitude BD is drawn to hypotenuse AC.  If BD = 4, AD = x - 6, and CD = x, what is the length of CD?

Accepted Answer

8

Answer

5

Answer

2

Answer

11

Question 57

In the diagram of ∆ABC,  DE || AC .  If EB is 3 more than DB, AB = 14, and CB = 21, what is the length of AD?

Accepted Answer

8

Answer

12

Answer

9

Answer

6

Question 58

In triangle ABC,  DE || AC and AD:DB = 3:5.  If DB = 6.3 and AC = 9.4, what is the length of DE, to the nearest tenth?

Accepted Answer

5.9

Answer

3.8

Answer

5.6

Answer

15.7

Question 59

In right triangle ABC shown, AC||DE.  If AB = 15, BC = 12, and EC = 7, what is the length of BD?

Accepted Answer

6.25

Answer

8.75

Answer

5

Answer

4

Question 60

Which proportion in relation to ∆ABC and ∆RST is NOT correct?

Accepted Answer

$\frac{AB}{RS}$ = $\frac{RT}{AC}$

Answer

$\frac{BC}{ST}$ = $\frac{AC}{RT}$

Answer

$\frac{BC}{ST}$ = $\frac{AB}{RS}$

Answer

$\frac{AB}{AC}$ = $\frac{RS}{RT}$

Question 61

If KG = 9 and IG = 12, the length of IM is

Accepted Answer

20

Answer

16

Answer

15

Answer

25

Question 62

If BD = 5, DA = 12, and BE = 7, what is the length of BC so that AC || DE?

Accepted Answer

23.8

Answer

8.6

Answer

16.8

Answer

15.6

Question 63

In ∆ABC shown, ∠ACB is a right angle, E is a point on AC, and ED is drawn perpendicular to hypotenuse AB.  If AB = 9, BC = 6, and DE =4, what is the length of AE?

Accepted Answer

6

Answer

8

Answer

7

Answer

5

Question 64

Determine and state, to the nearest tenth, the length of RQ.

Accepted Answer

13.2

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