AnswersMathematics IISimilarity Transformations

Similarity Transformations — Test Answers

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What are the coordinates of vertex cap j of the pre-image?

A
open paren 0 comma negative 4 close paren
B
open paren 0 comma 0 close paren
C
open paren 0 comma negative 1 close paren
D
open paren 0 comma 4 close paren
3

What is the value of x ?

A
12 units
B
25 units
C
20 units
D
15 units
5

On a number line, the directed line segment from cap q to cap s has endpoints cap q at negative 14 and cap s at 2 Point cap r partitions the directed line segment from cap q to cap s in a ratio of 3 to 5 ratio. Which expression correctly uses the formula open paren the fraction with numerator m and denominator m plus n close paren times open paren x sub 2 minus x sub 1 close paren plus x sub 1 to find the location of point cap r ?

A
open paren the fraction with numerator 3 and denominator 3 plus 5 close paren times open paren negative 14 minus 2 close paren plus 2
B
open paren the fraction with numerator 3 and denominator 3 plus 5 close paren times open paren 2 minus 14 close paren plus 14
C
open paren the fraction with numerator 3 and denominator 3 plus 5 close paren times open paren 2 minus negative 14 close paren plus negative 14
D
open paren the fraction with numerator 3 and denominator 3 plus 5 close paren times open paren negative 14 minus 2 close paren minus 2
7

Which best explains why all equilateral triangles are similar?

A
All equilateral triangles are congruent and therefore similar, with side lengths in a ratio of 1 to 1 ratio.
B
All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.
C
All equilateral triangles can be mapped onto each other using rigid transformations.
D
All equilateral triangles can be mapped onto each other using dilations.
8

What are the coordinates of the endpoints of the segment cap t prime cap v prime ?

A
cap t prime times open paren negative 3 comma 6 close paren and cap v prime times open paren 0 comma 3 close paren
B
cap t prime times open paren negative 1 comma 2 close paren and cap v prime times open paren 0 comma 1 close paren
C
cap t prime times open paren negative 1 comma 2 close paren and cap v prime times open paren 0 comma 3 close paren
D
cap t prime times open paren negative 3 comma 6 close paren and cap v prime times open paren 0 comma 1 close paren
9

Right triangle ABC is reflected over line segment AC , then dilated by a scale factor of 2 thirds to form triangle DEC Which statements about the two triangles must be true? Choose three correct answers.

A
3 m angle cap A is equal to 2 m angle cap d
B
2 m angle cap A is equal to 3 m angle cap d
C
3DE is equal to 2AB
D
3BC is equal to 2EC
E
triangle ABC approximates triangle DEC
F
angle cap b is congruent to angle cap e
10

What is the length of line segment SR ?

A
9 units
B
12 units
C
15 units
D
18 units
11

What is the value of y ?

A
3 square root of 3 units
B
12 square root of 3 units
C
6 square root of 3 units
D
9 square root of 3 units
15

What is the perimeter of triangle WXY ?

A
11 point 5 7 cm
B
12 point 4 6 cm
C
12 point 2 2 cm
D
14 point 5 0 cm
16

Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?

A
No, because corresponding sides have different slopes.
B
Yes, because both figures are rectangles and all rectangles are similar.
C
Yes, because corresponding sides are parallel and have lengths in the ratio 4 thirds .
D
No, because the center of dilation is not at open paren 0 comma 0 close paren .
17

Which statements are true? Choose three correct answers.

A
Segment EE prime is parallel to segment FF prime .
B
triangle DEF approximates triangle cap d prime cap e prime cap f prime
C
The measure of angle cap e prime is 1 third the measure of angle cap e .
D
The distance from point cap d prime to the origin is 1 third the distance of point cap d to the origin.
E
angle cap f corresponds to angle cap f prime .
18

Why is the information in the diagram enough to determine that triangle LMN approximates triangle PON using a rotation about point cap n and a dilation?

A
because angle MNL and angle ONP are congruent angles
B
because one pair of congruent corresponding angles is sufficient to determine similar triangles
C
because both triangles appear to be equilateral
D
because both triangles appear to be isosceles, angle MNL is congruent to angle ONP , and angle NOP is congruent to angle OPN
19

Which transformations could have occurred to map triangle ABC to triangle cap A double prime cap b double prime cap c double prime ?

A
a translation and a dilation
B
a dilation and a rotation
C
a rotation and a reflection
D
a reflection and a dilation
20

If triangle YWZ approximates triangle YXW , what is true about angle XWZ ?

A
angle XWZ is congruent to angle WXY .
B
angle XWZ is an obtuse angle.
C
angle XWZ is a right angle.
D
angle XWZ is congruent to angle XZW .

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